Symmetric strategy improvement is an algorithm introduced by Schewe et al. (ICALP 2015) that can be used to solve two-player games on directed graphs such as parity games and mean payoff games. In contrast to the usual well-known strategy improvement algorithm, it iterates over strategies of both players simultaneously. The symmetric version solves the known worst-case examples for strategy improvement quickly, however its worst-case complexity remained open. We present a class of worst-case examples for symmetric strategy improvement on which this symmetric version also takes exponentially many steps. Remarkably, our examples exhibit this behaviour for any choice of improvement rule, which is in contrast to classical strategy improvement where hard instances are usually hand-crafted for a specific improvement rule. We present a generalized version of symmetric strategy iteration depending less rigidly on the interplay of the strategies of both players. However, it turns out it has the same shortcomings.

Abstract We present an innovative approach to the reactive synthesis of parity automaton specifications, which plays a pivotal role in the synthesis of linear temporal logic. We find that our method efficiently solves the SYNTCOMP synthesis competition benchmarks for parity automata from LTL specifications, solving all 288 models in under a minute. We therefore direct our attention to optimizing the circuit size and propose several methods to reduce the size of the constructed circuits: (1) leveraging different parity game solvers, (2) applying bisimulation minimisation to the winning strategy, (3) using alternative encodings from the strategy to an and-inverter graph, (4) integrating post-processing with the ABC tool. We implement these methods in the Knor tool, which has secured us multiple victories in the PGAME track of the SYNTCOMP competition.

Java code can be annotated with formal specifications using the Java Modelling Language (JML). Previous work has provided IDE plugins intended to help write JML, but mostly for the Eclipse IDE. We introduce IntelliJML, a JML plugin for IntelliJ IDEA, with a focus on ease of use and maintainability. Features such as syntax, semantic, and type checking, as well as syntax highlighting and code completion are integrated into the plugin. The plugin can also be extended in the future to add more features. The source code for the plugin can be found at https://gitlab.utwente.nl/fmt/intellijml.

Deep neural networks have lead to a breakthrough in depth estimation from single images. Recent work shows that the quality of these estimations is rapidly increasing. It is clear that neural networks can see depth in single images. However, to the best of our knowledge, no work currently exists that analyzes what these networks have learned. In this work we take four previously published networks and investigate what depth cues they exploit. We find that all networks ignore the apparent size of known obstacles in favor of their vertical position in the image. The use of the vertical position requires the camera pose to be known; however, we find that these networks only partially recognize changes in camera pitch and roll angles. Small changes in camera pitch are shown to disturb the estimated distance towards obstacles. The use of the vertical image position allows the networks to estimate depth towards arbitrary obstacles - even those not appearing in the training set - but may depend on features that are not universally present.

The Model Checking Contest (MCC) is an annual competition of software tools for model checking. Tools must process an increasing benchmark gathered from the whole community and may participate in various examinations: state space generation, computation of global properties, computation of some upper bounds in the model, evaluation of reachability formulas, evaluation of CTL formulas, and evaluation of LTL formulas. For each examination and each model instance, participating tools are provided with up to 3600 s and 16 gigabyte of memory. Then, tool answers are analyzed and confronted to the results produced by other competing tools to detect diverging answers (which are quite rare at this stage of the competition, and lead to penalties). For each examination, golden, silver, and bronze medals are attributed to the three best tools. CPU usage and memory consumption are reported, which is also valuable information for tool developers.

Saturation is an efficient exploration order for computing the set of reachable states symbolically. Attempts to parallelize saturation have so far resulted in limited speedup. We demonstrate for the first time that on-the-fly symbolic saturation can be successfully parallelized at a large scale. To this end, we implemented saturation in Sylvan’s multi-core decision diagrams used by the LTSmin model checker. We report extensive experiments, measuring the speedup of parallel symbolic saturation on a 48-core machine, and compare it with the speedup of parallel symbolic BFS and chaining. We find that the parallel scalability varies from quite modest to excellent. We also compared the speedup of on-the-fly saturation and saturation for pre-learned transition relations. Finally, we compared our implementation of saturation with the existing sequential implementation based on Meddly. The empirical evaluation uses Petri nets from the model checking contest, but thanks to the architecture of LTSmin, parallel on-the-fly saturation is now available to multiple specification languages. Data or code related to this paper is available at: [ 34 ].

Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely believed to admit a polynomial solution, but so far no such algorithm is known. We propose a new algorithm to solve parity games based on learning tangles, which are strongly connected subgraphs for which one player has a strategy to win all cycles in the subgraph. We argue that tangles play a fundamental role in the prominent parity game solving algorithms. We show that tangle learning is competitive in practice and the fastest solver for large random games. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We introduce parallel symbolic algorithms for bisimulation minimisation, to combat the combinatorial state space explosion along three different paths. Bisimulation minimisation reduces a transition system to the smallest system with equivalent behaviour. We consider strong and branching bisimilarity for interactive Markov chains, which combine labelled transition systems and continuous-time Markov chains. Large state spaces can be represented concisely by symbolic techniques, based on binary decision diagrams. We present specialised BDD operations to compute the maximal bisimulation using signature-based partition refinement. We also study the symbolic representation of the quotient system and suggest an encoding based on representative states, rather than block numbers. Our implementation extends the parallel, shared memory, BDD library Sylvan, to obtain a significant speedup on multi-core machines. We propose the usage of partial signatures and of disjunctively partitioned transition relations, to increase the parallelisation opportunities. Also our new parallel data structure for block assignments increases scalability. We provide SigrefMC, a versatile tool that can be customised for bisimulation minimisation in various contexts. In particular, it supports models generated by the high-performance model checker LTSmin, providing access to specifications in multiple formalisms, including process algebra. The extensive experimental evaluation is based on various benchmarks from the literature. We demonstrate a speedup up to 95 $$\times $$ for computing the maximal bisimulation on one processor. In addition, we find parallel speedups on a 48-core machine of another 17 $$\times $$ for partition refinement and 24 $$\times $$ for quotient computation. Our new encoding of the reduced state space leads to smaller BDD representations, with up to a 5162-fold reduction.

The Hardware Model Checking Competition (HWMCC) 2017 affiliated to the International Conference on Formal Methods in Computer Aided Design (FMCAD) in 2017 in Vienna was the 9th competitive event for hardware model checkers we organized. After HWMCC'15 affiliated with FMCAD'15 in Austin, the competition took a break in 2016.

Binary decision diagrams are fundamental data structures in discrete mathematics, electrical engineering and computer science. Many different variations of binary decision diagrams exist, in particular variations that employ different reduction rules. For some applications, such as on-the-fly state space exploration, multiple reduction rules are beneficial to minimize the size of the involved graphs. We propose tagged binary decision diagrams, an edge-based approach that allows to use two reduction rules simultaneously. Experimental evaluations demonstrate that on-the-fly state space exploration is an order of magnitude faster using tagged binary decision diagrams compared to traditional binary decision diagrams.

Decision diagrams are used in symbolic verification to concisely represent state spaces. A crucial symbolic verification algorithm is reachability: systematically exploring all reachable system states. Although both parallel and distributed reachability algorithms exist, a combined solution is relatively unexplored. This paper contributes BDD-based reachability algorithms targeting compute clusters: high-performance networks of multi-core machines. The proposed algorithms may use the entire memory of every machine, allowing larger models to be processed while increasing performance by using all available computational power. To do this effectively, a distributed hash table, cluster-based work stealing algorithms, and several caching structures have been designed that all utilise the newest networking technology. The approach is evaluated extensively on a large collection of models, thereby demonstrating speedups up to 51,1x with 32 machines. The proposed algorithms not only benefit from the large amounts of available memory on compute clusters, but also from all available computational resources.

Decision diagrams, such as binary decision diagrams, multi-terminal binary decision diagrams and multi-valued decision diagrams, play an important role in various fields. They are especially useful to represent the characteristic function of sets of states and transitions in symbolic model checking. Most implementations of decision diagrams do not parallelize the decision diagram operations. As performance gains in the current era now mostly come from parallel processing, an ongoing challenge is to develop datastructures and algorithms for modern multi-core architectures. The decision diagram package Sylvan provides a contribution by implementing parallelized decision diagram operations and thus allowing sequential algorithms that use decision diagrams to exploit the power of multi-core machines. This paper discusses the design and implementation of Sylvan, especially an improvement to the lock-free unique table that uses bit arrays, the concurrent operation cache and the implementation of parallel garbage collection. We extend Sylvan with multi-terminal binary decision diagrams for integers, real numbers and rational numbers. This extension also allows for custom MTBDD leaves and operations and we provide an example implementation of GMP rational numbers. Furthermore, we show how the provided framework can be integrated in existing tools to provide out-of-the-box parallel BDD algorithms, as well as support for the parallelization of higher-level algorithms. As a case study, we parallelize on-the-fly symbolic reachability in the model checking toolset LTSmin . We experimentally demonstrate that the parallelization of symbolic model checking for explicit-state modeling languages, as supported by LTSmin , scales well. We also show that improvements in the design of the unique table result in faster execution of on-the-fly symbolic reachability.