TravMC2: higher-order model checking for alternating parity tree automata

Neatherway, Robin P.; Ong, C.-H. Luke

doi:10.1145/2632362.2632381

Cited by 8 publications

(2 citation statements)

References 16 publications

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“…We have carried out experiments to evaluate the efficiency of HomuSat. As benchmark problems, we used HORS model checking problems used as benchmarks for HORS model checkers TravMC2 [14], HorSatP [18], and Hor-Sat2 [8]. These benchmarks include many typical instances of higher-order model checking, such as the ones obtained from program verification problems.…”

Section: Implementation and Experimentsmentioning

confidence: 99%

A Type-Based HFL Model Checking Algorithm

Hosoi

Kobayashi

Tsukada

2019

Programming Languages and Systems

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Higher-order modal fixpoint logic (HFL) is a higher-order extension of the modal µ-calculus, and strictly more expressive than the modal µ-calculus. It has recently been shown that various program verification problems can naturally be reduced to HFL model checking: the problem of whether a given finite state system satisfies a given HFL formula. In this paper, we propose a novel algorithm for HFL model checking: it is the first practical algorithm in that it runs fast for typical inputs, despite the hyper-exponential worst-case complexity of the HFL model checking problem. Our algorithm is based on Kobayashi et al.'s type-based characterization of HFL model checking, and was inspired by a saturation-based algorithm for HORS model checking, another higherorder extension of model checking. We prove the correctness of the algorithm and report on an implementation and experimental results.The syntax of formulas on the first two lines is identical to that of the modal µ-calculus formulas, except that the variable X can range over higher-order predicates, rather than just propositions. Intuitively, µX η .ϕ (νX η .ϕ, resp.) denotes the least (greatest, resp.) predicate of type η such that X = ϕ. Higher-order predicates can be manipulated by using λ-abstractions and applications. The type o denotes the type of propositions. A type environment H for simple types is a map from a finite set of variables to the set of simple types. We often treat H as a set of type bindings of the form X : η, and write X : η ∈ H when H(X) = η. A type judgment relation H ⊢ ϕ : η is derived by the typing rules in Figure 1.

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Section: Implementation and Experimentsmentioning

confidence: 99%

A Type-Based HFL Model Checking Algorithm

Hosoi

Kobayashi

Tsukada

2019

Programming Languages and Systems

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“…From a practical standpoint, it may help building model-checking tools for µ-calculus specifications. Indeed, competitive and highly optimized tools exist for analysing reachability and safety properties of higher-order recursion schemes (HorSat [6,30,19] and Preface [27] being the current state-of-the-art), but implementing efficient tools for parity games remains a problem [15,22]. Having the reduction at hand can allow the use of safety tools for checking parity conditions, suggest the transfer of techniques and optimizations from safety to parity, and inspire new algorithms for parity games.…”

Section: Introductionmentioning

confidence: 99%

Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems

Hague,

Meyer,

Muskalla

et al. 2018

Preprint

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We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known since both problems are complete for the same complexity class. Coming up with a direct reduction, however, has been an open problem. Our solution to the puzzle brings together a number of techniques for pushdown games and adds three new ones. This work contributes to a recent trend of liveness to safety reductions which allow the advanced state-of-the-art in safety checking to be used for more expressive specifications. ACM Subject Classification:Theory of computation → Logic and verification, Theory of computation → Modal and temporal logics, Theory of computation → Verification by model checking, Theory of computation → Grammars and context-free languages.

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