Compositional higher-order model checking via
            <i>ω</i>
            -regular games over Böhm trees

Tsukada, Takeshi; Ong, C.-H. Luke

doi:10.1145/2603088.2603133

Cited by 22 publications

(20 citation statements)

References 20 publications

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“…This is in sharp contrast to what happens for non-probabilistic higher-order programs, for which model checking techniques can be fruitfully employed for proving both reachability and safety properties, as shown in the extensive literature on the subject (e.g. [55,32,44,46,48,31,30,64,59]). There have been some studies on the termination of probabilistic higher-order programs [16], but to our knowledge, they have not provided a procedure for precisely computing the termination probability, nor discussed whether it is possible at all: see Section 7 for more details.…”

Section: Introductionmentioning

confidence: 89%

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Kobayashi

Lago

Grellois

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs. In spite of the emergence of higher-order probabilistic programming languages, not much has been done to combine those two approaches. In this paper, we initiate a study on the probabilistic higher-order model checking problem, by giving some first theoretical and experimental results. As a first step towards our goal, we introduce PHORS, a probabilistic extension of higher-order recursion schemes (HORS), as a model of probabilistic higher-order programs. The model of PHORS may alternatively be viewed as a higher-order extension of recursive Markov chains. We then investigate the probabilistic termination problem -or, equivalently, the probabilistic reachability problem. We prove that almost sure termination of order-2 PHORS is undecidable. We also provide a fixpoint characterization of the termination probability of PHORS, and develop a sound (but possibly incomplete) procedure for approximately computing the termination probability. We have implemented the procedure for order-2 PHORSs, and confirmed that the procedure works well through preliminary experiments that are reported at the end of the article.

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Section: Introductionmentioning

confidence: 89%

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Kobayashi

Lago

Grellois

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…We, therefore, use intersection types (a la Kobayashi and Ong's intersection types for HORS model checking [21]) to represent summary information on how each function traverses states of the automaton, and replicate each function and its arguments for each type. We thus formalize the translation as an intersection-type-based program transformation; related transformation techniques are found in [8,11,12,20,38]. …”

Section: Example 10 Consider the Automatonmentioning

confidence: 99%

Higher-Order Program Verification via HFL Model Checking

Kobayashi

Tsukada

Watanabe

2018

Lecture Notes in Computer Science

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Abstract. There are two kinds of higher-order extensions of model checking: HORS model checking and HFL model checking. Whilst the former has been applied to automated verification of higher-order functional programs, applications of the latter have not been well studied. In the present paper, we show that various verification problems for functional programs, including may/must-reachability, trace properties, and linear-time temporal properties (and their negations), can be naturally reduced to (extended) HFL model checking. The reductions yield a sound and complete logical characterization of those program properties. Compared with the previous approaches based on HORS model checking, our approach provides a more uniform, streamlined method for higher-order program verification.

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“…[37,44,54]), a higher-order recursion scheme (HORS) generates an infinite tree that is then model-checked against a modal µ-formula. The generated tree is in general irrationalhence cannot be identified with a finite-state automaton.…”

Section: Establishing An Alternating Fixed-point In Theorem Provingmentioning

confidence: 99%

Lattice-theoretic progress measures and coalgebraic model checking

Hasuo

Shimizu

Cîrstea

2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this paper we identify the essence of this workflow to be the notion of progress measure, and formalize it in general, possibly infinitary, lattice-theoretic terms. Our view on progress measures is that they are to nested/alternating fixed points what invariants are to safety/greatest fixed points, and what ranking functions are to liveness/least fixed points. That is, progress measures are combination of the latter two notions (invariant and ranking function) that have been extensively studied in the context of (program) verification.We then apply our theory of progress measures to a general model-checking framework, where systems are categorically presented as coalgebras. The framework's theoretical robustness is witnessed by a smooth transfer from the branching-time setting to the linear-time one. Although the framework can be used to derive some decision procedures for finite settings, we also expect the proposed framework to form a basis for sound proof methods for some undecidable/infinitary problems.

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Compositional higher-order model checking via ω -regular games over Böhm trees

Cited by 22 publications

References 20 publications

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Higher-Order Program Verification via HFL Model Checking

Lattice-theoretic progress measures and coalgebraic model checking

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