As quantum software engineering advances, testing techniques are required to assess the quality of quantum programs (QPs). In the test process, the test oracle is vital for determining whether the test result indicates a success or a failure. Most related works directly measure the output states and acquire the corresponding test results by comparing the output distribution with the expected one. While attention has been paid to the capability of fault detection, the guarantee for the correctness of the produced test results remains limited. Unlike classical programs (CPs), the output quantum states of QPs should be transformed into probabilistic classical outcomes through quantum measurement. This additional operation of measurement could cause a test oracle to yield the wrong test results. Especially for high-dimensional output spaces, numerous measurement outcomes are required to capture the distribution characteristics, threatening the effectiveness and cost-efficiency of test oracles. Hence, this paper proposes a novel specified test oracle DOSS employing a dynamic scheme to integrate a quantum algorithm (i.e., swap test) with the direct measurement mode. This innovative approach enables the validation of individual outputs rather than their distribution during the testing phase. Considering acceptable cost, DOSS decomposes the fully or partially separable output states to lower the dimensionality and simplify the quantum circuit for testing. Empirical studies demonstrate that DOSS generally gives more correct test results than baselines, and maintains reasonable cost on an ideal simulator. Besides, DOSS’s effectiveness with quantum noise involved is validated via three noisy simulators.

Quantum computing has recently experienced rapid advancements and promised transformative applications across many fields. To promote the real-world applications of quantum computing, application-oriented quantum programs (AQPs) are designed to explore quantum hardware in performing substantial computational tasks and promote practical use cases for quantum computing. The complexity and scalability of AQPs, along with their dependence on advanced quantum algorithms, make them particularly challenging to understand and maintain. Clear comments offer an effective means of elucidating core logic and filling the knowledge gap for developers unfamiliar with quantum mechanics. Research on code comment for QPs remains scarce, highlighting the need for further investigation into effective comment methods for these complex programs. Given the potential advantages of large language models (LLMs), including their contextual understanding and language generation capabilities, LLMs can significantly reduce the cost of manual comment. Thus, this paper proposes a framework called QuAInth, which utilizes LLMs to annotate AQPs. This framework begins by preprocessing AQPs and segmenting them based on functional signatures. It then employs prompts (i.e., textual instructions carefully structured and given to LLMs) of varying granularity to guide comment generation. Aside from two existing text-based metrics, QuAInth newly adopts a quantum-specific metric that considers 8 indicators to evaluate the domainrelated correctness and clarity of the generated comments. Finally, with the understanding that an individual LLM may produce wrong outputs, QuAInth proposes a vote-enhanced fusion scheme inspired by N-version programming, in which distinct comments output from multiple LLMs are fused into a more reliable and comprehensive comment. Empirical studies are conducted with 4 AQPs written by Qiskit and 3 prevailing open-source LLMs (i.e., Qwen, DeepSeek-Coder, and Llama). The empirical results demonstrate the effectiveness of QuAInth, showing that the fused comments outperform those generated by individual models in the vast majority of cases.

With the rapid development of uncrewed aerial vehicle (UAV) technology in recent years, research on large-scale low-altitude UAV air traffic management (ATM) has gained attention. Unlike the traditional ATM, the number of small UAVs in the airspace may be in the millions, making air traffic management challenging. In an ATM, airspace is composed of airways, intersections, and nodes. In this paper, a three-dimensional (3-D) roundabout model is utilized as an airspace structure for air traffic intersections of known traffic network models, which is decomposed into a central island, several ramps, and buffer zones. In this paper, for simplicity, the distributed coordination of the motions of Vertical TakeOff and Landing (VTOL) UAVs to pass through a 3-D roundabout is focused on, which is formulated as a 3-D roundabout passing-through problem. The corresponding control objectives include inter-agent conflict-free, keeping within the 3-D curved virtual tube, and avoiding local minima. Lyapunov-like functions are designed elaborately, and formal analysisismade to show that all UAVs can pass through the 3-D roundabout without getting trapped. Taking the kinematic model of VTOL UAVs into consideration, the horizontal control and attitude control channels are decoupled, which is more reasonable for practical applications. Numerical simulation and real experiment are given to show the effectiveness of the proposed method.

Due to the growing demand for high-quality quantum programs (QPs), unit testing is employed to check the behavior of QPs. As for quantum inputs of testing, most studies limit test inputs to pure states, whereas mixed states representing probabilistic mixtures of pure states are almost excluded from the test process. Besides, when achieving the input domain coverage, lots of pure-state test cases (PSTCs) with pure states as inputs should be employed, leading to high time costs for testing. To handle that, this article explores using mixed states as test inputs for better utilization of quantum information. From the perspective of input domain coverage, applying mixed-state test cases (MSTCs) replacing PSTCs can simplify the test suite and accordingly promote test efficiency. Owing to the mixture of multiple pure states, a single MSTC is more likely to detect a fault than a PSTC, thereby enhancing test effectiveness. This article then proposes a unit testing framework, including generation and execution of MSTCs. Also, this article presents two guidelines and two parameterized quantum circuits to prepare desired mixed states. Empirical studies evaluate the performance of MSTCs and the experimental results demonstrate that MSCTs generally consume less time and detect more faults than PSTCs.

In V-SLAM, the estimation of relative camera pose is crucial to determine the spatial relationship between consecutive camera images, helping to accurately track the movement of the camera in its environment. In small indoor scenes, when the training set is limited, which is very common in robot SLAM, learning-based methods may fail to converge, especially the Transformer architecture, which requires a more substantial dataset to match the performance of the CNN architecture model. This work addresses this problem with the sharing attention mechanism, building on recent improvements in solving visual Transformer architectures on small datasets while incorporating messenger tokens. Besides, double-embedding is introduced to capture the spatial of images and order of images. In summary, we introduce an intuitive end-to-end relative pose estimation solution and prove its accuracy on the two smallest sub-datasets of 7Scenes. The proposed method is tested with a set of comparison experiments conducted across CNN-based, Transformer-based end-to-end relative pose estimation models, and the robust feature-matching non-learning method. Our model outperforms in all comparisons. Furthermore, ablation studies clearly illustrate that these innovations are crucial for the accuracy of relative pose estimation on small datasets.

Quantum Computing (QC) leverages quantum mechanics to manipulate quantum information, holding greater potential than classical computing. To fully exploit QC’s potential, it is crucial to ensure the reliability and quality of quantum programs. Research on quantum program testing is still at its early stage, in which some distinctive features of quantum programs, e.g., superposition and entanglement, may be overlooked, and the fault detection capability and testing effectiveness are rather limited. Besides, the input space of quantum programs may exponentially grow when the number of qubits increases, posing great challenges to testing quantum programs. It is imperative to develop a proper testing strategy to effectively select the potential failure-causing test cases and detect faults faster. In this paper, test cases with both basis states and superposition ones are considered and generated to cover more input space. A hybrid distance measurement method based on quantum fidelity and Hamming distance is presented for measuring the similarity among quantum test cases. Furthermore, a Dynamic Random Testing strategy based on Hybrid distance metrics (DRT-H) for quantum programs is proposed, which combines the hybrid distance metrics and the feedback mechanism of the classical Dynamic Random Testing (DRT) strategy to adjust the testing profile and guide the test case selection. Experimental studies demonstrate that the proposed DRT-H strategy outperforms the baseline testing strategies in most cases.

With the continuous advancement of quantum computing (QC), the demand for high-quality quantum programs (QPs) is growing. To avoid program failure, in software engineering, the technology of automatic program repair (APR) employs appropriate patches to remove potential bugs without the intervention of a human. However, the method tailored for repairing defective QPs is still absent. This article proposes, to the best of our knowledge, a new APR method named UnitAR that can repair QPs via unitary operation automatically. Based on the characteristics of superposition and entanglement in QC, the article constructs an algebraic model and adopts a generate-and-validate approach for the repair procedure. Furthermore, the article presents two schemes that can respectively promote the efficiency of generating patches and guarantee the effectiveness of applying patches. For the purpose of evaluating the proposed method, the article selects 29 mutated versions as well as five real-world buggy programs as the objects and introduces two traditional APR approaches GenProg and TBar as baselines. According to the experiments, UnitAR can fix 23 buggy programs, and this method demonstrates the highest efficiency and effectiveness among three APR approaches. Besides, the experimental results further manifest the crucial roles of two constituents involved in the framework of UnitAR .

Unmanned Aerial Vehicles (UAVs) are now becoming increasingly accessible to amateur and commercial users alike. Several types of airspace structures have been proposed in recent research, which include several structured free flight concepts. In this paper, for simplicity, distributed coordination of the motions of cooperative multicopters in structured airspace concepts is focused on. This is formulated as a free flight problem, including convergence to destination lines/planes and inter-agent collision avoidance. The destination line of each multicopter is known a priori. Further, Lyapunov-like functions are designed elaborately, while formal analysis and proofs of the proposed distributed control are given to show that the free flight control problem can be solved. What is more, by the proposed controller, a multicopter can keep away from another as soon as possible once it enters the safety area of another one. Simulations and experiments are given to show the effectiveness of the proposed method.

Unmanned aerial vehicles are now becoming increasingly accessible to amateur and commercial users alike. A safety air traffic management system is needed to help ensure that every newest entrant into the sky does not collide with others. Much research has been done to design various methods to perform collision avoidance with obstacles. However, how to decide the safety radius subject to communication uncertainties is still suspended. Based on assumptions on communication uncertainties and supposed control performance, a separation principle of the safety radius design and controller design is proposed. With it, the safety radius in the design phase (without uncertainties) and flight phase (subject to uncertainties) are studied. Furthermore, the results are extended to multiple obstacles. Simulations and experiments are carried out to show the effectiveness of the proposed methods.

This study proposes auniformpassivefault-tolerant control (FTC) method for a quadcopter that does not rely on fault information subject to one, two adjacent, two opposite, or three rotor failure. Theuniformcontrol implies that thepassiveFTC is able to cover the condition from quadcopter fault-free to rotor failure without the need for controller switching. To achieve the purpose ofpassiveFTC, the fault of rotors is modeled as a lumped disturbance acting on the virtual control of the quadcopter system. The estimated disturbance is used directly in thepassiveFTC. At the same time, a modified controller structure is designed to achieve the passive FTC ability for two and three rotor failure. To avoid the control allocation switching from the fault-free control to the FTC, a dynamic control allocation is used. In addition, the closed-loop stability is analyzed in the presence of up to three rotor failure. To validate the proposeduniformpassiveFTC method, outdoor experiments are performedfor the first time, which have demonstrated that the hovering quadcopter is able to recover from one rotor failure using the proposed controller and resume its mission even if two adjacent, two opposite, or three rotors fail, without the need for any rotor fault information or controller switching. Experimental results can be viewed in this video:https://youtu.be/N1OudPXFXnE. Source code is placed onhttps://github.com/RflyBUAA/DegradedControl.git

[J1C2 Presentation Abstract at IEEE SERVICES 2022 for IEEE Transactions on Services Computing, 2022, 15(2):736-751. DOI: 10.1109/TSC.2019.2960496].

The traditional multicopter design method usually requires a long iterative process to find the optimal design based on given performance requirements. The method is uneconomical and inefficient. In this article, a practical method is proposed to automatically calculate the optimal multicopter design according to the given design requirements including flight time, altitude, payload capacity, and maneuverability. The proposed method contains two algorithms, including an off-line algorithm and an online algorithm. The off-line algorithm finds the optimal components (propeller and electronic speed controller) for each motor to establish its component combination, and subsequently, these component combinations and their key performance parameters are stored in a combination database. The online algorithm obtains the multicopter design results that satisfy the given requirements by searching through the component combinations in the database and calculating the optimal parameters for the battery and airframe. Subsequently, these requirement-satisfied multicopter design results are obtained and sorted according to an objective function that contains evaluation indexes, including size, weight, performance, and practicability. The proposed method has the advantages of high precision and quick calculating speed because parameter calibrations and time-consuming calculations are completed offline. Experiments are performed to validate the effectiveness and practicality of the proposed method. Comparisons with the brutal search method and other design methods demonstrate the efficiency of the proposed method.Note to Practitioners—The proposed method is fast and practical to obtain an optimal solution by only using a low-performance web server, and the algorithm has been published online athttp://www.flyeval.com/recalc.htmlto provide an online optimization design service for users. To make it convenient to apply the proposed method to multicopter designs, the propulsion system combination database obtained by our off-line algorithm is released along with the article. This database includes more than 1500 experimentally calibrated propulsion combinations, which are adequate for readers to use the proposed optimization algorithms to design multicopters with weights (sizes) ranging from 0.2 to 50 kg.

Unmanned Aerial Vehicles (UAVs) are now becoming increasingly accessible to amateur and commercial users alike. The main task for UAVs is to keep a prescribed separation with obstacles in the air. In this paper, a collision-avoidance control method for non-cooperative moving obstacles is proposed for a multicopter with the altitude hold mode by using a Lyapunov-like barrier function. Lyapunov-like functions are designed elaborately, based on which formal analysis and proofs of the proposed control are made to show that the collision-avoidance control problem can be solved if the moving obstacle is slower than the multicopter. The result can be extended to some cases of multiple obstacles. What is more, by the proposed control, a multicopter can keep away from obstacles as soon as possible, once obstacles enter into the safety area of the multicopter accidentally, and converge to the waypoint. Simulations and experiments are given to show the effectiveness of the proposed method by showing the distance between UAV and waypoint, obstacles respectively.

In recent years, service oriented architecture (SOA) has been increasingly adopted to develop distributed applications in the context of the Internet. To develop reliable SOA-based applications, an important issue is how to ensure the quality of web services. In this article, we propose a dynamic random testing (DRT) technique for web services, which is an improvement over the widely-practiced random testing (RT) and partition testing (PT) approaches. We examine key issues when adapting DRT to the context of SOA, including a framework, guidelines for parameter settings, and a prototype for such an adaptation. Empirical studies are reported where DRT is used to test three real-life web services, and mutation analysis is employed to measure the effectiveness. Our experimental results show that, compared with the three baseline techniques, RT, Adaptive Testing (AT) and Random Partition Testing (RPT), DRT demonstrates higher fault-detection effectiveness with a lower test case selection overhead. Furthermore, the theoretical guidelines of parameter setting for DRT are confirmed to be effective. The proposed DRT and the prototype provide an effective and efficient approach for testing web services.

One goal of software testing strategies is to detect faults faster. Dynamic Random Testing (DRT) strategy uses the testing results to guide the selection of test cases, which have shown to be effective in the fault detection process. However, the effectiveness of DRT still can be improved. In this paper, a distance-based DRT (D-DRT) strategy is proposed. The vectorized test cases are partitioned with k-means clustering method to obtain better classification, and the distance information are used to guide the test case selection, then the test cases that are close to failure-causing test cases are more likely to be selected, thus the testing process can be optimized. In the case study, the performance of D-DRT and other testing strategies are compared. The experiment results show that the proposed D-DRT strategy has better fault detection effectiveness than the others without significant increase in computational cost.

Random testing and partition testing are two major families of software testing techniques. They have been compared both theoretically and empirically in numerous studies for decades, and it has been widely acknowledged that they have their own advantages and disadvantages and that their innate characteristics are fairly complementary to each other. Some work has been conducted to develop advanced testing techniques through the integration of random testing and partition testing, attempting to preserve the advantages of both while minimizing their disadvantages. In this paper, we propose a new testing approach, adaptive partition testing, where test cases are randomly selected from some partition whose probability of being selected is adaptively adjusted along the testing process. We particularly develop two algorithms, Markov-chain based adaptive partition testing and reward-punishment based adaptive partition testing, to implement the proposed approach. The former algorithm makes use of Markov matrix to dynamically adjust the probability of a partition to be selected for conducting tests; while the latter is based on a reward and punishment mechanism. We conduct empirical studies to evaluate the performance of the proposed algorithms using ten faulty versions of three large-scale open source programs. Our experimental results show that, compared with two baseline techniques, namely random partition testing (RPT) and dynamic random testing (DRT), our algorithms deliver higher fault-detection effectiveness with lower test case selection overhead. It is demonstrated that the proposed adaptive partition testing is an effective testing approach, taking advantages of both random testing and partition testing.

A particularly good software testing strategy is to achieve the underlying testing goal while solving the problems of tradeoffs between testing effectiveness and efficiency. To improve the fault detection effectiveness of software testing, the principle of feedback control theory was adopted, which motivated the proposal of dynamic random testing (DRT). The main idea behind DRT is using the testing results to guide the test case selection to increase the selection probabilities of the subdomains with higher fault detection rates. Previous works show that DRT strategy can achieve better effectiveness than random testing strategy and random partition testing strategy, and has significantly lower computational costs than adaptive testing strategy. However, the essential factors that affect the performance of DRT, i.e., adjusting parameters, initial profile, and test case classification have not been thoroughly investigated. Besides, some experimental assumptions are inconsistent with real scenarios. Therefore, this paper gives a series of investigations on DRT with a set of practical subject programs. More specifically, the effectiveness and efficiency of DRT are presented, and the extended experiments on DRT with relevant factors are conducted. The results indicate that the effectiveness of DRT is robust to different initial profiles and affected noticeably by the adjusting parameter settings and test case classification methods.

The Android operating system (OS) is a sophisticated man-made system and is the dominant OS in the current smartphone market. Due to the accumulation of errors in the system internal state and the incremental consumption of resources, such as the Dalvik heap memory of software applications and the physical memory, software aging is observed frequently and recognized as a chronic problem of Android smartphones. To mitigate this problem, we propose a two-level software rejuvenation, with the two levels referring to software applications and the OS, in this paper. Based on this strategy, a Markov regenerative process model is constructed to evaluate the steady-state availability and to optimize the time required to trigger rejuvenation for Android smartphones. The parameters of the model, such as the degradation rate and failure rate of software applications and the Android OS, are obtained via our testing platform. Experiments on two real Android applications show that the availability of an Android smartphone increases by 10.81% and 10.18% for the two subjects in our experiments, respectively. An empirical study comparing our two-level strategy with one-level strategies (single application-level and system-level rejuvenation) further verifies the effectiveness of our approach.

This paper presents an empirical study of 5741 bug reports for the Linux kernel from an evolutionary perspective, with the aim of obtaining a deep understanding of bug characteristics in the Linux operating system. Bug classification is performed based on the fault triggering conditions, followed by an analysis of the proportions and evolution of the bug types as well as comparisons among versions, products, and repair locations. In addition, an analysis of regression bugs and the relationship between the types of bugs and the time needed to fix them are presented. Moreover, a procedure for the analysis of bug type characteristics based on complex network metrics is proposed, and four network metrics, i.e., degree, clustering coefficient, betweenness, and closeness, are utilized to further investigate the relationship between bug types and software metrics. In this paper, 22 interesting findings based on the empirical results are revealed, and guidance based on these findings is provided for developers and users.

Service disruptions due to deliberate sabotage are serious threats to supply systems. To alleviate the loss of accessibility caused by such disruptions, identifying the system vulnerabilities that would be worth strengthening is a critical problem in critical infrastructure protection. Today's supply systems tend to be organized in a decentralized manner, with different components belonging to different entities, keeping much information private. Therefore, a protection plan must balance its benefits among these entities for universal agreement to be reached. This paper addresses the issue of decentralized supply chain fortification by proposing the R-Interdiction Median problem with Fortification for Decentralized supply systems (D-RIMF). In the D-RIMF, each demand node is private and is a client of a certain facility; each facility evaluates its potential worst-case reduction in accessibility, measured as the increase in service provision costs considering only its own clients, and the objective is to minimize the largest evaluation values. To model the D-RIMF, we introduce a bilevel multiagent framework, in which all facilities and the defender are considered as independent agents. To solve the D-RIMF, both heuristic and optimal algorithms are designed to satisfy different requirements. Finally, the usefulness of the D-RIMF and the performances of the proposed algorithms are observed through simulations performed on typical datasets.

Due to the advantages of cloud computing, it has been adopted as deployment platform of SBS (Service-based Systems). It also provides an elastic "pay-as-you-go" mode, which creates new resource allocation challenge that satisfying the QoS (Quality of Service) requirements with least resource allocation. There has been much interest in using feedback control to make resource allocation, but these works focus on a single control that does not take the interactions between servers share and compete for the same resource pool. In this paper, we present an adaptive resource allocation approach for SBS in the cloud environment using MIMO (Multi-Input and Multi-Output) control to allocate resource to multiple servers according to multiple workloads. The experimental results show that our approach can ensure the QoS with least resource allocation and increase the resource utilization.

Linux operating system is a complex system that is prone to suffer failures during usage, and increases difficulties of fixing bugs. Different testing strategies and fault mitigation methods can be developed and applied based on different types of bugs, which leads to the necessity to have a deep understanding of the nature of bugs in Linux. In this paper, an empirical study is carried out on 5741 bug reports of Linux kernel from an evolution perspective. A bug classification is conducted based on fault triggering conditions, followed by the analysis of the evolution of bug type proportions over versions and time, together with their comparisons across versions, products and regression bugs. Moreover, the relationship between bug type proportions and clustering coefficient, as well as the relation between bug types and time to fix are presented. This paper reveals 13 interesting findings based on the empirical results and further provides guidance for developers and users based on these findings.

In the process of continuous operation in a software system, a series of phenomena could lead to performance degradation of the system, namely software aging. The loss caused by software aging can be reduced through proper rejuvenation strategies, the key to which is to determine the rejuvenation thresholds. Essence of some traditional methods is to set predetermined thresholds based on empirical data. However, in some systems where the memory is shared between operating system and application software (two-granularity software system), as the memory consumption is closely related to system performance and changes constantly, using empirical thresholds may cause system outage or waste of resources. In this paper, an adaptive strategy is adopted to optimize the thresholds. Instead of fixed thresholds, the method regularly regulates the thresholds by taking feedback information in the running process into account. Especially, critical equations are constructed to calculate the thresholds by maximizing the system availability. Simulation results show that the proposed method achieves higher availability and more stable performance than that based on empirical thresholds.

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely, that the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. In order to avoid such a singularity, a new projection matrix is proposed based on which a feasible point method to continuous-time, equality-constrained optimization is developed. First, the equality constraint is transformed into a continuous-time dynamical system with solutions that always satisfy the equality constraint. Second, a new projection matrix without singularity is proposed to realize the transformation. An update (or say a controller) is subsequently designed to decrease the objective function along the solutions of the transformed continuous-time dynamical system. The invariance principle is then applied to analyze the behavior of the solution. Furthermore, the proposed method is modified to address cases in which solutions do not satisfy the equality constraint. Finally, the proposed optimization approach is applied to three examples to demonstrate its effectiveness.

Software rejuvenation is a proactive software control technique that is used to improve a computing system performance when it suffers from software aging. In this paper, a two-granularity inspection-based software rejuvenation policy, which works as a closed-loop control technique, is proposed. This policy mitigates the negative impact of two-level software aging. The two levels considered are the user-level applications and the operating system. A Markov regenerative process model is constructed based on the system condition. We obtain the degradation rate of the application software and operating system from fault injection experiments. The diagnostic accuracy of the adopted monitor and analysis system, which is applied to inspect the application software and operating system, is considered as we provide the optimal rejuvenation strategies. Finally, the availability and the overall loss probability with their corresponding optimal inspection time intervals are obtained numerically based on the parameter values estimated from the experiments. Experimental results show that two-granularity software rejuvenation is much more effective than traditional single-level software rejuvenation. In our experimental study, when two-granularity software rejuvenation is used, the unavailability and the overall loss probability of the system were reduced by 17.9% and 2.65%, respectively, in comparison with the single-level rejuvenation.

Fault Localization Prioritization (FLP) aims at reordering existing test cases so that the location of detected faulty components can be identified earlier, using certain fault localization techniques. Although some researchers have proposed adaptive prioritization strategies with white-box code coverage information, such information may not always be available. In this paper, we address the FLP problem using black-box information derived from partitioning the input domain. Based on the well-known technique of Spectra-Based Fault Localization (SBFL), three test case prioritization strategies are designed following some basic SBFL heuristics. The implementation of these proposed strategies relies only on the partition information, and does not require any test case execution history. Experiments show that our strategies, when compared with pure random selection, result in a faster localization of faulty statements, reducing the number of test case executions required. Here, we analyze the characteristics and merits of the three proposed strategies.

Debugging is an indispensable yet frustrating activity in software development and maintenance. Thus, numerous techniques have been proposed to aid this task. Despite the demonstrated effectiveness and future potential of these techniques, many of them have the unrealistic single-fault failure assumption. To alleviate this problem, we propose a technique that can be used to distinguish failing tests that executed a single fault from those that executed multiple faults in this paper. The technique suitably combines information from (i) a set of fault localization ranked lists, each produced for a certain failing test and (ii) the distance between a failing test and the passing test that most resembles it to achieve this goal. An experiment on 5 real-life medium-sized programs with 18, 920 multiple-fault versions, which are shipped with number of faults ranging from 2 to 8, has been conducted to evaluate the technique. The results indicate that the performance of the technique in terms of evaluation measures precision, recall, and F-measure is promising. In addition, for the identified failing tests that executed a single fault, the technique can also properly cluster them.

Fish‐eye cameras are becoming increasingly popular in computer vision, but their use for three‐dimensional measurement is limited partly because of the lack of an accurate, efficient and user‐friendly calibration procedure. For such a purpose, the authors propose a method to calibrate the intrinsic and extrinsic parameters (including radial distortion parameters) of two/multiple fish‐eye cameras simultaneously by using a wand under general motions. Thanks to the generic camera model used, the proposed calibration method is also suitable for two/multiple conventional cameras and mixed cameras (e.g. two conventional cameras and a fish‐eye camera). Simulation and real experiments demonstrate the effectiveness of the proposed method. Moreover, the authors develop the camera calibration toolbox, which is available online.

Software aging refers to the phenomenon that software systems show progressive performance degradation or a sudden crash after longtime execution. It has been reported that this phenomenon is closely related to the exhaustion of system resources. This paper quantitatively studies available system resources under the real-world situation where workload changes dynamically over time. We propose a neural network approach to first investigate the relationship between available system resources and system workload and then to forecast future available system resources. Experimental results on data sets collected from real-world computer systems demonstrate that the proposed approach is effective.

Prognostics and health management (PHM) technology has been widely accepted, and employed to evaluate system performance. In practice, system performance often varies continually rather than just being functional or failed, especially for a complex system. Profust reliability theory extends the traditional binary state space {0, 1} into a fuzzy state space [0, 1], which is therefore suitable to characterize a gradual physical degradation. Moreover, in profust reliability theory, fuzzy state transitions can also help to describe the health evolution of a component or a system. Accordingly, this paper proposes a profust reliability based PHM approach, where the profust reliability is employed as a health indicator to evaluate the real-time system performance. On the basis of the health estimation, the system remaining useful life (RUL) is further defined, and the mean RUL estimate is predicted by using a degraded Markov model. Finally, an experimental case study of Li-ion batteries is presented to demonstrate the effectiveness of the proposed approach.

In software reliability assessment, one problem of interest is how to minimize the variance of reliability estimator, which is often considered as an optimization goal. The basic idea is that an estimator with lower variance makes the estimates more predictable and accurate. Adaptive Testing (AT) is an online testing strategy, which can be adopted to minimize the variance of software reliability estimator. In order to reduce the computational overhead of decision-making, the implemented AT strategy in practice deviates from its theoretical design that guarantees AT's local optimality. This work aims to investigate the asymptotic behavior of AT to improve its global performance without losing the local optimality. To this end, a new AT strategy named Adaptive Testing with Gradient Descent method (AT-GD) is proposed. Theoretical analysis indicates that AT-GD, a locally optimal testing strategy, converges to the globally optimal solution as the assessment process proceeds. Simulation and experiments are set up to validate AT-GD's effectiveness and efficiency. Besides, sensitivity analysis of AT-GD is also conducted in this study.

Random testing (RT) and subdomain testing are two major software testing strategies. Their simplicity makes them likely the most efficient testing strategies with respect to the time required for test case selection. However, the disadvantage of RT is its defect detection effectiveness. Adaptive testing (AT) is a feedback-based software testing strategy that has been shown to be more effective than RT and partition testing (PT). However, a major concern in the application of AT is its complexity and computational cost for test case selection. In this paper, we propose a hybrid approach that uses AT and random partition testing (RPT) in an alternating manner. The motivation for this approach is that both strategies are employed such that the underlying computational complexity of AT is reduced by introducing RPT into the testing process without affecting the defect detection effectiveness. A case study with seven real-life subject programs is presented. The experimental results demonstrate that this novel strategy considerably reduces the computational overhead of the original AT strategy but still outperforms the pure RT strategy and PT strategy in terms of the number of test cases used to detect and remove a given number of defects. In addition, a sensitivity analysis is conducted to validate the robustness of our strategy.

Test case prioritization (TCP) techniques aim to schedule the order of regression test suite to maximize some properties, such as early fault detection. In order to measure the abilities of different TCP techniques for early fault detection, a metric named average percentage of faults detected (APFD) is widely adopted. In this paper, we analyze the metric APFD and explore the gain of measuring TCP techniques from a control theory viewpoint. Based on that, we propose a generalized metric for TCP. This new metric focuses on the gain of defining early fault detection and measuring TCP techniques for various needs in different evaluation scenarios. By adopting this new metric, not only flexibility can be guaranteed, but also explicit physical significance for the metric will be provided before evaluation.

In recent years, Service Oriented Architecture (SOA) has been increasingly adopted to develop applications in the context of Internet. To develop reliable SOA-based applications, an important issue is how to ensure the quality of Web services. In this paper, we propose a dynamic random testing (DRT) technique for Web services which is an improvement of the widely practiced random testing. We examine key issues when adapting DRT to the context of SOA and develop a prototype for such an adaptation. Empirical studies are reported where DRT is used to test two real-life Web services and mutation analysis is employed to measure the effectiveness. The experimental results show that DRT can save up to 24% test cases in terms of detecting the first seeded fault, and up to 21% test cases in terms of detecting all seeded faults, both with the cases of uniformed mutation analysis and distribution-aware mutation analysis, which refer to faults being seeded in an even or clustered way, respectively. The proposed DRT and the prototype provide an effective approach to testing Web Services.

The five papers in this special section focus on computational intelligence in reliability engineering.

A complex fuzzy relation is defined as a fuzzy relation whose membership function takes values in the unit circle on a complex plane. This paper first investigates various operation properties of a complex fuzzy relation. It then defines the distance measure of two complex fuzzy relations that can measure the differences between the grades as well as the phases of two complex fuzzy relations. This distance measure is used to define δ-equalities of complex fuzzy relations that coincide with those of fuzzy relations already defined in the literature if complex fuzzy relations reduce to real-valued fuzzy relations. Two complex fuzzy relations are said to be δ-equal if the distance between them is less than 1-δ. This paper shows how various operations between complex fuzzy relations, including T-norms and S-norms, affect given δ-equalities of complex fuzzy relations. Finally, fuzzy inference is examined in the framework of delta- equalities of complex fuzzy relations.

A major advantage of service-based computing technology is the ability to enable rapid formation of distributed computing systems by composing massively available services over various types of networks. Their confidentiality and privacy should be well protected under various situations. This paper proposed a control-based approach to balance the trade-off between security and performance of adaptive service-based systems (ASBS). The relationship between encryption/decryption delay and the content size for cryptographic algorithms providing different security levels are measured and modeled. An example application based on the ASBS prototype is implemented to demonstrate the effectiveness of the proposed approach.

Adaptive testing is the counterpart of adaptive control in software testing. It means that software testing strategy should be adjusted on-line by using the testing data collected during software testing as our understanding of the software under test improves. In doing so, online estimation of parameters plays a crucial role. In this paper, we investigate the computational complexity of the parameter estimation process in two adaptive testing strategies which adopt different parameter estimation methods, namely the genetic algorithm (GA) method and the recursive least square estimation (RLSE) method. Theoretical analysis and simulations are conducted to compare the asymptotic complexity and the runtime overhead of the two adaptive testing strategies. Finally, a controlled experiment on the space program is conducted to measure the relationship between computational complexity and the failure detection efficiency for the two strategies.

Adaptive testing is the counterpart of adaptive control in software testing. It means that software testing strategy should be adjusted on-line by using the testing data collected during software testing as our understanding of the software under test is improved. Previous studies on adaptive testing involved a simplified Controlled Markov Chain (CMC) model for software testing which employs several unrealistic assumptions. In this paper we propose a new adaptive software testing approach in the context of an improved and namely, general CMC model which aims to eliminate such threats to validity. A set of more realistic basic assumptions on the software testing process is proposed and several unrealistic assumptions are replaced by less unrealistic assumptions. A new adaptive testing strategy based on the general CMC is developed and implemented. Mathematical simulations and experiments on real life software are conducted to demonstrate the effectiveness of the new strategy.

Service-oriented architecture (SOA) for distributed computing has become increasingly popular due to the big advantage that distributed applications can be rapidly synthesized with the needed services provided by various service providers through heterogeneous networks. Systems based on SOA are called Service-based Systems (SBS), and a special variety of SBS, namely the Adaptive Service-Based Systems (ASBS), is aimed to be adaptable to constantly changing user requirements, environments and resource constraints. An important and difficult issue is how to design and develop ASBS to satisfy multiple QoS requirements in an open dynamic environment. In this paper, inspired by the underlying principle of hierarchical intelligent control, a three-layer architecture for developing and deploying ASBS is presented to address this issue. Compared with existing architectures for SBS, the advantage of using our architecture is that it provides the flexibility for system designers to adopt different control based approaches to guarantee user requirements and satisfy resource constraints at different levels of the system. Moreover, our architecture enables the system to take hierarchical adaptation actions at runtime to avoid possible violation of user requirement or resource constraint. An example is given to illustrate how to adopt our architecture to guide the design of a simple ASBS, and preliminary experimental data are presented to demonstrate the feasibility of developing ASBS based on our architecture.

Software aging refers to the phenomenon that the performance degradation, increasing failure rate or massive resource usage demonstrated in long-running software systems such as web servers. It was reported that software aging has a significant relationship with resource usage. To study the software aging phenomenon in web servers, we built an experimental platform with a server and multiple clients to collect the data of system resource usage on the server. In this paper, we present several experiments based on the platform and study software aging phenomenon of a widely used web server software system – the Apache HTTP server. Some repeatable software aging phenomena are observed in our experiments. The process of software aging is shown to be nonlinear and chaotic. In order to better present the nonlinear interplay of various resource parameters of web server and forecast resource exhaustion, a nonlinear dynamic model of software aging is constructed to formulate software aging process.

Adaptive software testing is the counterpart of adaptive control in software testing. It means that software testing strategy should be adjusted online by using the testing data collected during software testing as our understanding of the software under test improves. Previous studies on adaptive testing rely on a simplified Controlled Markov Chain (CMC) model for software testing which employs several unrealistic assumptions. In this paper we propose a new adaptive software testing approach in the context of an improved CMC model which aims to eliminate such threats to validity. A new set of basic assumptions on the software testing process is proposed and several unrealistic assumptions are replaced by more common situations in real life software testing. The methodology of a new adaptive testing strategy is also developed and implemented. Experimental data are collected to demonstrate the effectiveness of the new methodology.

Service-oriented architecture (SOA) for distributed computing has become increasingly popular due to the great advantage that distributed applications can be rapidly synthesized with the needed services provided by various service providers through broadband networks. Systems based on SOA are called service-based systems (SBS). An important and difficult issue is how to develop SBS adaptable to constantly changing user requirements, environments and resource constraints. In this paper, an intelligent control architecture is presented to address this issue. This architecture has three layers based on the intelligent control theory for developing and deploying SBS. An example to illustrate the intelligent control architecture for adaptive SBS is given and preliminary experimental data is presented to demonstrate the feasibility of our approach.

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Software cybernetics is an emerging area that explores the interplay between software and control. The controlled Markov chain (CMC) approach to software testing supports the idea of software cybernetics by treating software testing as a control problem, where the software under test serves as a controlled object modeled by a controlled Markov chain and the software testing strategy serves as the corresponding controller. The software under test and the corresponding software testing strategy form a closed-loop feedback control system. The theory of controlled Markov chains is used to design and optimize the testing strategy in accordance with the testing/reliability goal given explicitly and a priori. Adaptive software testing adjusts and improves software testing strategy online by using the testing data collected in the course of software testing. In doing so, the online parameter estimations play a key role. In this paper, we study the effects of genetic algorithm and the gradient method for doing online parameter estimation in adaptive software testing. We find that genetic algorithm is effective and does not require prior knowledge of the software parameters of concern. Although genetic algorithm is computationally intensive, it leads the adaptive software testing strategy to an optimal software testing strategy that is determined by optimizing a given testing goal, such as minimizing the total cost incurred for removing a given number of defects. On the other hand, the gradient method is computationally favorable, but requires appropriate initial values of the software parameters of concern. It may lead, or fail to lead, the adaptive software testing strategy to an optimal software testing strategy, depending on whether the given initial parameter values are appropriate or not. In general, the genetic algorithm should be used instead of the gradient method in adaptive software testing. Simulation results show that adaptive software testing does work and outperforms random testing.

Different from the dominant view of treating fuzzy reasoning as generalization of classical logical inference, in this paper fuzzy reasoning is treated as a control problem. A new fuzzy reasoning method is proposed that employs an explicit feedback mechanism to improve the robustness of fuzzy reasoning. The fuzzy rule base given a priori serves as a controlled object, and the fuzzy reasoning method serves as the corresponding controller. The fuzzy rule base and the fuzzy reasoning method constitute a control system that may be open loop or closed loop, depending on the underlying reasoning goals/constraints. The fuzzy rule base, the fuzzy reasoning method, and the corresponding reasoning goals/constraints define the three distinct ingredients of fuzzy reasoning. While various existing fuzzy reasoning methods are essentially a static mapping from the universe of single fuzzy premises to the universe of single fuzzy consequences, the new fuzzy reasoning method maps sequences of fuzzy premises to sequences of fuzzy consequences and is a function of the underlying reasoning goals/constraints. The Monte Carlo simulation shows that the new fuzzy reasoning method is much more robust than the optimal fuzzy reasoning method proposed in our previous work. The explicit feedback mechanism embedded in the fuzzy reasoning method does significantly improve the robustness of fuzzy reasoning, which is concerned with the effects of perturbations associated with given fuzzy rule bases and/or fuzzy premises on fuzzy consequences. The work presented in this paper sets a new starting point for various principles of feedback control and optimization to be applied in fuzzy reasoning or logical inference and to explore new forms of reasoning including robust reasoning and adaptive reasoning. It can be also expected that the new fuzzy reasoning method presented in this paper can be used for modeling and control of complex systems and for decision-making under complex environments.

Software defects play a key role in software reliability, and the number of remaining defects is one of most important software reliability indexes. Observing the trend of the number of remaining defects during the testing process can provide very useful information on the software reliability. However, the number of remaining defects is not known and has to be estimated. Therefore, it is important to study the trend of the remaining software defect estimation (RSDE). In this paper, the concept of RSDE curves is proposed. An RSDE curve describes the dynamic behavior of RSDE as software testing proceeds. Generally, RSDE changes over time and displays two typical patterns: 1) single mode and 2) multiple modes. This behavior is due to the different characteristics of the testing process, i.e., testing under a single testing profile or multiple testing profiles with various change points. By studying the trend of the estimated number of remaining software defects, RSDE curves can provide further insights into the software testing process. In particular, in this paper, the Goel-Okumoto model is used to estimate this number on actual software failure data, and some properties of RSDE are derived. In addition, we discuss some theoretical and application issues of the RSDE curves. The concept of the proposed RSDE curves is independent of the selected model. The methods and development discussed in this paper can be applied to any valid estimation model to develop and study its corresponding RSDE curve. Finally, we discuss several possible areas for future research.

The problem of reliable H(infinity) nonuniform sampling fuzzy control for nonlinear systems with time delay is investigated in this paper. Utilizing the input delay approach and the descriptor model transformation, an equivalent continuous-time generalized Takagi-Sugeno fuzzy system is obtained. Sufficient conditions for the existence of state feedback controller are derived in terms of linear matrix inequities (LMIs), which guarantee the requirements of H( infinity) performance criterion for the normal and possible actuator fault cases. In order to relax the conservatism of these obtained conditions, a feasible algorithm is provided to remove some slightly restricted conditions in LMIs. Finally, an illustrative example is given to show the validity of the proposed scheme.

Non-functional computing should be developed in parallel with functional computing. In order to do so, a plausible starting point is to examine non-functional attributes of existing computing models. A finite state machine (FSM) specifies one or more accept states.

In data stream management systems (DSMSs), request handling has to meet various QoS requirements. Traditional open-loop DSMS ignores system status information and run-time history in decision making and is unable to achieve stable QoS performance over run-time as the workload or environment changes. This paper discusses the design of a close-loop DSMS that applies adaptive control in control theory to adapt itself to the changing environment and workloads in order to optimize the QoS performance over run-time. The proposed adaptive DSMS is built on system identification and successive approximation knowledge in control theory and uses a least square approach for parameter estimation. Experimental data shows that the proposed adaptive DSMS outperforms the traditional open-loop DSMS in overall QoS among various network conditions and workload settings.

Localizing a bug in a program can be a complex and timeconsuming process. In this paper we propose a code coveragebased fault localization method to prioritize suspicious code in terms of its likelihood of containing program bugs. Code with a higher risk should be examined before that with a lower risk, as the former is more suspicious (i.e., more likely to contain program bugs) than the latter. We also answer a very important question: How can each additional test case that executes the program successfully help locate program bugs? We propose that with respect to a piece of code, the aid introduced by the first successful test that executes it in computing its likelihood of containing a bug is larger than or equal to that of the second successful test that executes it, which is larger than or equal to that of the third successful test that executes it, etc. A tool, ÷Debug, was implemented to automate the computation of the risk of the code and the subsequent prioritization of suspicious code for locating program bugs. A case study using the Siemens suite was also conducted. Data collected from our study support the proposal described above. They also indicate that our method (in particular Heuristics III (c), (d), and (e)) can effectively reduce the search domain for locating program bugs.

A software system can be modeled by a transition system. In the existing approaches for software modeling, such as FSM, EFSM, and TM etc., states often have specific physics semantics which often represent variables, processes, or modules, etc. In this paper, a data mining approach is introduced into software modeling to do state definition in a different way. The approach is used to extract interesting relationships among program methods and a weighted hypergraph is constructed based on the mining results. Then the hypergraph is partitioned into k clusters which are used to define states in the transition system, using a hypergraph partitioning algorithm. States derived in this way have many particular properties. Some experiments about this approach are also presented in this paper.

Previous works on GUI testing are mainly concerned with how to define or generate GUI test cases. The issue of how to employ generated GUI test cases or primitive actions is seldom discussed. In this paper we propose a dynamic partitioning approach for GUI testing to address the issue. In this approach, the given GUI primitive actions are dynamically partitioned into two disjoint classes: one comprising prioritized primitive actions and the other comprising non-prioritized ones. The testing process is divided into two stages and contains two feedback loops. The first stage prioritizes primitive actions and the second stage selects and performs prioritized primitive actions. The first feedback loop is local and occurs in the second stage, which adjusts the memberships of primitive actions after they are performed. The second feedback loop is global and occurs between the first and second stages. It switches GUI testing from the second stage to the first stage upon no prioritized primitive actions are available. Two testing experiments with real GUI applications show that the proposed dynamic partitioning approach can really work in practice and may significantly outperform the random testing approach in the sense that the dynamic partitioning approach uses fewer primitive actions to achieve given testing goals and behaves more stable. The dynamic partitioning approach adopts explicit feedback mechanisms and contributes to the emerging area of software cybernetics that explores the interplay between software and control.

Software reliability is one of the key factors for determining the quality of software, and a number of software reliability models have been developed for measuring it, among which a group of Markov-based models prevails. In fact, the Markovian assumption can also widely observed in performance evaluation of software system. In this paper, an experimental approach is used to check if GUI software structural profile, which is defined as transfer of control among software modules or states, possesses Markovian property, utilizing x2hypothesis test. The result of the case study indicates that the structural profile of GUI software fails to fit a Markov process

This paper is concerned with the robust-stabilization problem of uncertain Markovian jump nonlinear systems (MJNSs) without mode observations via a fuzzy-control approach. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. The aim is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system (MJFS) is robustly stochastically stable. Based on a stochastic Lyapunov function, a robust-stabilization condition using a mode-independent fuzzy controller is derived for the uncertain MJFS in terms of linear matrix inequalities (LMIs). A new improved LMI formulation is used to alleviate the interrelation between the stochastic Lyapunov matrix and the system matrices containing controller variables in the derivation process. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.

A new partition testing strategy that adopts dynamic partitioning is proposed in this paper. By dynamic partitioning it is meant that the test suite or the input domain of the software under test is partitioned into several subdomains whose members are dynamically adjusted during testing by using feedback information such as the testing data collected on-line. Two controlled software experiments show that the new strategy can significantly outperform the purely random testing strategy in particular, and the random-partition testing strategy in general.

A fuzzified radial basis function network (FRBFN) is a kind of fuzzy neural network that is obtained by direct fuzzification of the well known neural model RBFN. A FRBFN contains fuzzy weights and can handle fuzzy-in fuzzy-out data. This paper shows that a FRBFN can also be interpreted as a kind of fuzzy expert system. Hence it owns the advantages of simple structure and clear physical meaning. Some metrics for fuzzy numbers have been extended to the metrics for n-dimensional fuzzy vectors, which are applicable to computations in FRBFNs. The corresponding metric spaces for n-dimensional fuzzy vectors are proved to be complete. Further, FRBFNs are proved to be able to act as universal function approximators for any continuous fuzzy function defined on a compact set. This paper applies the proposed FRBFN to nonparametric fuzzy nonlinear regression problems for multidimensional LR-type fuzzy data. Fuzzy nonlinear regression with FRBFNs can be formulated as a nonlinear mathematical programming problem. Two training algorithms are proposed to quickly solve the two types of problems under different criteria and constraint conditions, namely, the two-stage and BP (Back-Propagation) training algorithms. Simulation studies are carried out to verify the feasibility and demonstrate the advantages of the proposed approaches.

Many fuzzy control schemes used in industrial practice today are based on some simplified fuzzy reasoning methods, which are simple but at the expense of losing robustness, missing fuzzy characteristics, and having inconsistent inference. The concept of optimal fuzzy reasoning is introduced in this paper to overcome these shortcomings. The main advantage is that an integration of the optimal fuzzy reasoning with a PID control structure will generate a new type of fuzzy-PID control schemes with inherent optimal-tuning features for both local optimal performance and global tracking robustness. This new fuzzy-PID controller is then analyzed quantitatively and compared with other existing fuzzy-PID control methods. Both analytical and numerical studies clearly show the improved robustness of the new fuzzy-PID controller.

Fuzzy reasoning methods are extensively used in intelligent systems and fuzzy control. Most existing fuzzy reasoning methods follow rules of logical inference. In this article, fuzzy reasoning is treated as an optimization problem. The idea of optimal fuzzy reasoning is reviewed and three new optimal fuzzy reasoning methods are given by using new optimization objective functions. The robustness of fuzzy reasoning, that is, how errors in premises affect conclusions in fuzzy reasoning, is evaluated in a probabilistic or statistical context by using the Monte Carlo simulation method. Six optimal fuzzy reasoning methods are evaluated in comparison with the CRI method in terms of probabilistic robustness. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1033–1049, 2004.

Software defect curves describe the behavior of the estimate of the number of remaining software defects as software testing proceeds. They are of two possible patterns: single-trapezoidal-like curves or multiple-trapezoidal-like curves. In this paper we present some necessary and/or sufficient conditions for software defect curves of the Goel-Okumoto NHPP model. These conditions can be used to predict the effect of the detection and removal of a software defect on the variations of the estimates of the number of remaining defects. A field software reliability dataset is used to justify the trapezoidal shape of software defect curves and our theoretical analyses. The results presented in this paper may provide useful feedback information for assessing software testing progress and have potentials in the emerging area of software cybernetics that explores the interplay between software and control.

In this paper, we design an intelligent and robust stable fuzzy proportional-derivative (PD) controller for lateral control of passenger cars. An additional lateral displacement sensor is added at the tail bumper instead of gyro sensor in order to measure the yaw rate. First, a genetic-algorithm (GA)-based fuzzy PD controller is proposed to combine heuristics and optimization. Then, the fuzzy control system is transformed into a Lur'e system with uncertainties. The Lyapunov's direct method is used to guarantee the stability of the perturbed Lur'e system, and then a robustness measurement that gives the bound of the uncertainties is derived. The performance of the proposed controller is compared with a conventional PD controller through simulation studies. Experimental studies on a small-scale vehicle are also reported.

A collection of one or more devices, each described by its digital device manual and reachable over a network, is a ConnectedSpace. A set of safety policies may be enforced on a ConnectedSpace to ensure the safety of the environment in which the ConnectedSpace is deployed. The enforcement of these safety policies by one or more safely controllers governs the behavior of the devices within the ConnectedSpace. We propose a policy-based partitioning scheme for synthesizing k distributed safety controllers such that: (a) each device is guaranteed to be controlled by no more than two controllers, and (b) each policy is guaranteed to be enforced by exactly one controller. We present an experimental evaluation of our scheme. The experimental results show that the scheme is scalable with respect to the number of devices and the number of policies. We also show how safety controllers that are correct with respect to the policies, are synthesized using the theory of supervisory control.

Fuzzy reasoning methods (or approximate reasoning methods) are extensively used in intelligent systems and fuzzy control. In this paper the author discusses how errors in premises affect conclusions in fuzzy reasoning, that is, he discusses the robustness of fuzzy reasoning. After reviewing his previous work (1996), he presents robustness results for various implication operators and inference rules. All the robustness results are formulated in terms of /spl delta/-equalities of fuzzy sets. Two fuzzy sets are said to be /spl delta/-equal if they are equal to an extent of /spl delta/.