Abstract We consider equational theories based on axioms for recursively defining functions, with rules for equality and substitution, but no form of induction—we denote such equational theories as PETS for pure equational theories with substitution. An example is Cook’s system PV without its rule for induction. We show that the Bounded Arithmetic theory $\mathrm {S}^{1}_2$ proves the consistency of PETS. Our approach employs model-theoretic constructions for PETS based on approximate values resembling notions from domain theory in Bounded Arithmetic, which may be of independent interest.

Because human movement spreads infection, and mobility is a good proxy for other social distancing measures, human mobility has been an important factor in the COVID19 epidemic. Therefore, the control of human mobility is one of the countermeasures used to suppress an epidemic.As a notable feature, COVID19 has had multiple waves (subepidemics). Understanding the causes of the start and end of each wave has important implications for a policy evaluation and the timely implementation of countermeasures. Some of the waves have been correlated with the changes in mobility, and some can be attributed to the emergence of new variants. However, the start and end of some of the waves are difficult to explain through known factors.To evaluate the effect of human mobility, we built a stochastic model incorporating individual movements of 500,000 people obtained from anonymized, user-approved location data of smartphones throughout Japan. Instead of using aggregate values of human mobility, our model tracks the movements of individuals and predicts the infection of all persons within the entire country. Although the model only has a single static parameter, it successfully reproduced the occurrence of three waves of the number of confirmed cases within the study period of March 01 to December 31, 2020 in Japan. It was previously difficult to explain the end of the second wave and the start of the third wave in the study period by human mobility alone. Our results suggest the importance of tracking individual movements instead of relaying the aggregate values of human mobility.

Although researchers have created many advanced code-clone detection techniques, more effort is required to realize wide adaptation of these techniques in the industry. One of the reasons behind this is the reliance of these advanced techniques on lexing and parsing programs. Modern programming languages have complex lexical conventions and grammar, which evolve constantly. Therefore, using advanced code-clone detection techniques requires substantial and continuous effort. This paper proposes a lightweight language-independent method to detect code clones by simply finding repeated strings in a code repository, relying on neither lexing nor parsing. The proposed method is based on an efficient technique developed in a bio-informatics context to find repeated strings. We refer to the repeated strings in the source-code as weak Type-1 clones. Because the proposed technique normalizes newlines, tabs, and white spaces into a single white space, it can find clones in which newline positions or indentations are changed, as often in the case when copy-pasting occurs. Although the proposed method only finds verbatim copies, it also makes interesting observations regarding repository structures. Many developers may prefer the proposed simple approach because it is easier to understand than other advanced techniques that use heuristics, approximation, and machine learning.

ACyber-Physical System(CPS) is a system which consists of software components and physical components. Traditional system verification techniques such as model checking or theorem proving are difficult to apply to CPS because the physical components have infinite number of states. To solve this problem, robustness guided falsification of CPS is introduced. Robustness measures how robustly the given specification is satisfied. Robustness guided falsification tries to minimize the robustness by changing inputs and parameters of the system. The input with a minimal robustness (counterexample) is a good candidate to violate the specification. Existing methods use several optimization techniques to minimize robustness. However, those methods do not use temporal structures in a system input and often require a large number of simulation runs to minimize the robustness. In this paper, we explore state-of-the-artDeep Reinforcement Learning(DRL) techniques, i.e.,Asynchronous Advantage Actor-Critic(A3C) andDouble Deep Q Network(DDQN), to reduce the number of simulation runs required to find such counterexamples. We theoretically show how robustness guided falsification of a safety property is formatted as a reinforcement learning problem. Then, we experimentally compare the effectiveness of our methods with three baseline methods, i.e., random sampling, cross entropy and simulated annealing, on three well known CPS systems. We thoroughly analyse the experiment results and identify two factors of CPS which make DRL based methods better than existing methods. The most important factor is the availability of the system internal dynamics to the reinforcement learning algorithm. The other factor is the existence of learnable structure in the counterexample.

Abstract This article presents a proof that Buss’s $S_2^2$ can prove the consistency of a fragment of Cook and Urquhart’s PV from which induction has been removed but substitution has been retained. This result improves Beckmann’s result, which proves the consistency of such a system without substitution in bounded arithmetic $S_2^1$ . Our proof relies on the notion of “computation” of the terms of PV. In our work, we first prove that, in the system under consideration, if an equation is proved and either its left- or right-hand side is computed, then there is a corresponding computation for its right- or left-hand side, respectively. By carefully computing the bound of the size of the computation, the proof of this theorem inside a bounded arithmetic is obtained, from which the consistency of the system is readily proven. This result apparently implies the separation of bounded arithmetic because Buss and Ignjatović stated that it is not possible to prove the consistency of a fragment of PV without induction but with substitution in Buss’s $S_2^1$ . However, their proof actually shows that it is not possible to prove the consistency of the system, which is obtained by the addition of propositional logic and other axioms to a system such as ours. On the other hand, the system that we have considered is strictly equational, which is a property on which our proof relies.

Modbat makes testing easier by providing a user-friendly modeling language to describe the behavior of systems, from such a model, test cases are generated and executed. Modbat's domain-specific language is based on Scala, its features include probabilistic and non-deterministic transitions, component models with inheritance, and exceptions. We demonstrate the versatility of Modbat by finding a confirmed defect in the currently latest version of Java, and by testing SAT solvers.

Abstract The extended hierarchical state transition matrices (EHSTMs) are a table-based modelling language frequently used in industry for specifying behaviours of systems. However, assuring correctness, i.e., having a design satisfy certain desired properties, is a non-trivial task. To address this problem, a model checker dedicated to EHSTMs called Garakabu2 has been developed. However, there is no formal justification for Garakabu2, since its semantics has never been fully formalised. In this paper, we give a formal semantics to EHSTMs by translating them into CSP, Communicating Sequential Processes. Among the variants of CSP, we use CSP#, which is the modelling language used by PAT model checker, as a target of translation. Our semantics covers most of the features supported by Garakabu2. We manually translate the small examples of EHSTMs to CSP#, and verify them by PAT. We also verify the examples directly using Garakabu2 and show that the results are same. The experiments also indicate that verification using our translation and PAT is much faster than that of Garakabu2 in some cases.

Hierarchical State Transition Matrix (HSTM) is a table-based modeling language for developing designs of software systems. We have proposed a Satisfiability Modulo Theory (SMT) based Bounded Model Checking (BMC) approach in [1] to provide formal verification supports for conducting rigorous and automatic analysis to improve reliability of HSTM designs. In this paper, we continue that work by developing and evaluating approaches to accelerating BMC of HSTM designs. The approaches center around an unrolled Bounded Reach ability Tree (BRT) of a HSTM design that is built with stateless explicit state exploration. Specifically, reach ability of invalid cells (representing undesired states) of a HSTM design, which occurs within the bound concerned, could be discovered during construction of the BRT, and furthermore, if no such occurrence, the constructed BRT could be utilized to rule out unnecessary subformulas of a BMC instance for verification of LTL properties. We have implemented these approaches in a tool called Garakabu2 with the state-of-the-art SMT solver CVC3 as its back-ended solver. Our preliminary experiments show that verification could be accelerated substantially.