Solving games via three-valued abstraction refinement

Alfaro, Luca de; Roy, Pritam

doi:10.1016/j.ic.2009.05.007

Cited by 23 publications

(33 citation statements)

References 16 publications

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“…These ideas are relevant and could be helpful in several variants of CEGAR: in model checking of quantitative specifications, where the query is not binary [7], in a CEGAR method for µ-calculus, where formulas need not have a universal or existential polarity [18], in attempts to refine the three-valued semantics [3], and in algorithms that gather batches of counterexamples before refining [14,15].…”

Section: Discussionmentioning

confidence: 99%

An Abstraction-Refinement Framework for Trigger Querying

Avni

Kupferman

2011

Static Analysis

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Abstract. Trigger querying is the problem of finding, given a system M and an LTL formula ϕ, the set of scenarios that trigger ϕ in M ; that is, the language L of finite computations of M such that all infinite computations that have a prefix in L continue with a suffix that satisfies ϕ. For example, the trigger query M |=? → F err asks for the set of scenarios after which err aught to eventually happen. Trigger querying thus significantly extends query checking, which seeks propositional solutions, and is an extremely useful methodology for system exploration and understanding. The weakness of trigger querying lies in the fact that the size of the solution is linear in the size of the system. For trigger querying to become feasible in practice, we must offer solutions to cope with systems of big, and possibly infinite, state spaces. In this paper we describe an abstraction-refinement framework for trigger querying. The general idea is to replace the reasoning about M by reasoning about an abstraction MA of M , and return to the user two languages, L l and Lu, that under-and over-approximate L, respectively. We consider predicate abstraction, and the languages L l and Lu are defined with respect to the set of predicates. The challenge in defining the approximating languages is that trigger querying does not have a clear polarity, and the definition of L l and Lu has to combine the upper-and over-approximations of M . We describe an automata-theoretic approach for refining and reducing Lu \ L l . While refinement for model checking is lengthwise, in the sense that it is based on counterexamples, here we suggest both lengthwise and widthwise refinement, where the latter is based on cuts in an automaton for Lu \ L l and thus can symbolically handle batches of counterexamples. We show that our framework is robust and can be applied also for classical query checking as well as variants and extensions of trigger querying.

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Section: Discussionmentioning

confidence: 99%

An Abstraction-Refinement Framework for Trigger Querying

Avni

Kupferman

2011

Static Analysis

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“…After the initial submission, every tool is tested on a small set of benchmarks from the SYNTCOMP library, and authors are informed about any problems and can submit bugfixes. 1 Ranking Schemes. In all tracks, there is a ranking based on the number of correctly solved problems: a correct answer within the timeout of 3600s is rewarded with one point for the solver, and a wrong answer is punished by subtracting 4 points.…”

Section: General Rulesmentioning

confidence: 99%

“…Simple BDD Solver implements the standard BDD-based algorithm for safety games, including a large number of optimizations in configuration (basic). The other two configurations additionally implement an abstraction-refinement approach inspired by de Alfaro and Roy [1] in two variants: with overapproximation of the winning region in configuration (abs1), or with both over-and underapproximation in (abs2). The version entered into SYNTCOMP 2017 is the same as last year.…”

Section: Re-entered: Simple Bdd Solvermentioning

confidence: 99%

The 4th Reactive Synthesis Competition (SYNTCOMP 2017): Benchmarks, Participants & Results

Jacobs

Basset

Bloem

et al. 2017

Electron. Proc. Theor. Comput. Sci.

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We report on the fourth reactive synthesis competition (SYNTCOMP 2017). We introduce two new benchmark classes that have been added to the SYNTCOMP library, and briefly describe the benchmark selection, evaluation scheme and the experimental setup of SYNTCOMP 2017. We present the participants of SYNTCOMP 2017, with a focus on changes with respect to the previous years and on the two completely new tools that have entered the competition. Finally, we present and analyze the results of our experimental evaluation, including a ranking of tools with respect to quantity and quality of solutions.

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“…The first, which corresponds to A [6,16,18,21,22], where games combine may and must transitions, and also in settings in which games that are determined are approximated by means other than abstraction. For example, when LTL realizability is done by checking the realizability of approximations of both the specification and its negation [7].…”

Section: Introductionmentioning

confidence: 99%

Making Weighted Containment Feasible: A Heuristic Based on Simulation and Abstraction

Avni

Kupferman

2012

Lecture Notes in Computer Science

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Abstract. Weighted automata map input words to real numbers and are useful in reasoning about quantitative systems and specifications. The containment problem for weighted automata asks, given two weighted automata A and B, whether for all words w, the value that A assigns to w is less than or equal to the value B assigns to w. The problem is of great practical interest, yet is known to be undecidable. Efforts to approximate weighted containment by weighted variants of the simulation pre-order still have to cope with large state spaces. One of the leading approaches for coping with large state spaces is abstraction. We introduce an abstraction-refinement paradigm for weighted automata and show that it nicely combines with weighted simulation, giving rise to a feasible approach for the containment problem. The weighted-simulation pre-order we define is based on a quantitative two-player game, and the technical challenge in the setting origins from the fact the values that the automata assign to words are unbounded.The abstraction-refinement paradigm is based on under-and over-approximation of the automata, where approximation, and hence also the refinement steps, refer not only to the languages of the automata but also to the values they assign to words.

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Solving games via three-valued abstraction refinement

Cited by 23 publications

References 16 publications

An Abstraction-Refinement Framework for Trigger Querying

An Abstraction-Refinement Framework for Trigger Querying

The 4th Reactive Synthesis Competition (SYNTCOMP 2017): Benchmarks, Participants & Results

Making Weighted Containment Feasible: A Heuristic Based on Simulation and Abstraction

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