A Saturation Method for Collapsible Pushdown Systems

Broadbent, Chris; Carayol, Arnaud; Hague, Matthew; Serre, Olivier

doi:10.1007/978-3-642-31585-5_18

Cited by 35 publications

(39 citation statements)

References 28 publications

(28 reference statements)

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“…3 In other words, given s ∈ Stacks n , (s, s) ∈ r T L if and only if s ∈ L. We denote by T n the set of test operations over Stacks n . We enrich our basic operations over ST n with T n−1 .…”

Section: Normalised Automatamentioning

confidence: 99%

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Rewriting Higher-Order Stack Trees

Penelle

2017

Theory Comput Syst

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Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for monadic second order logic (respectively first order logic with a reachability predicate) is decidable on such graphs. We unify both models by introducing the notion of stack trees, trees whose nodes are labelled by higher-order stacks, and define the corresponding class of higher-order ground tree rewriting systems. We show that these graphs retain the decidability properties of ground tree rewriting graphs while generalising the pushdown hierarchy of graphs.

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Section: Normalised Automatamentioning

confidence: 99%

“…right) of both a test and a non-test transition, we get that θ 1 , θ 2 and θ 3 are empty operation, and thus that s = s 1 , s = s 2 , s = s 3 , and we did not add them any incoming edge (resp. output edge), the same reasoning apply to show there is no RTrans K (resp.…”

Section: Trans and Rtransmentioning

confidence: 99%

Rewriting Higher-Order Stack Trees

Penelle

2017

Theory Comput Syst

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“…Recently Broadbent et al [4] have introduced an algorithm based on collapsible pushdown automata (CPDA) [8]-which are equi-expressive with HORS-and implemented in the tool CSHORe [5]. Given an input co-trivial tree automaton, the algorithm uses a generalisation of the saturation algorithm for pushdown automata to compute the "pre-image" of the final error configurations, and checks if it includes the start state.…”

Section: Related Workmentioning

confidence: 99%

“…$15.00. http://dx.doi.org /10.1145/2535838.2535873 It is for these reasons, and despite the severe worst-case complexity of the problem 1 , that several ingenious algorithms [3,4,12,13,19] have recently been developed with the aim of solving the higher-order model checking problem for many "practical" instances. However, the state of this effort is summarised well by the authors of [3]:…”

Section: Introductionmentioning

confidence: 99%

A type-directed abstraction refinement approach to higher-order model checking

Ramsay

Neatherway

Ong

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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The trivial-automaton model checking problem for higher-order recursion schemes has become a widely studied object in connection with the automatic verification of higher-order programs. The problem is formidably hard 1 : despite considerable progress in recent years, no decision procedures have been demonstrated to scale robustly beyond recursion schemes that comprise more than a few hundred rewrite rules. We present a new, fixed-parameter polynomial time algorithm, based on a novel, type directed form of abstraction refinement in which behaviours of a scheme are distinguished by the abstraction according to the intersection types that they inhabit (the properties that they satisfy). Unlike other intersection type approaches, our algorithm reasons both about acceptance by the property automaton and acceptance by its dual, simultaneously, in order to minimize the amount of work done by converging on the solution to a problem instance from both sides. We have constructed PREFACE, a prototype implementation of the algorithm, and assembled an extensive body of evidence to demonstrate empirically that the algorithm readily scales to recursion schemes of several thousand rules, well beyond the capabilities of current stateof-the-art higher-order model checkers.

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“…We recently extended the saturation method to a backward reachability analysis of collapsible pushdown systems [7]. This runs in PTIME when the number of control states is bounded.…”

Section: Introductionmentioning

confidence: 99%

C-SHORe

et al. 2013

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Higher-order recursion schemes (HORS) have recently received much attention as a useful abstraction of higher-order functional programs with a number of new verification techniques employing HORS model-checking as their centrepiece. This paper contributes to the ongoing quest for a truly scalable model-checker for HORS by offering a different, automata theoretic perspective. We introduce the first practical model-checking algorithm that acts on a generalisation of pushdown automata equi-expressive with HORS called collapsible pushdown systems (CPDS). At its core is a substantial modification of a recently studied saturation algorithm for CPDS. In particular it is able to use information gathered from an approximate forward reachability analysis to guide its backward search. Moreover, we introduce an algorithm that prunes the CPDS prior to model-checking and a method for extracting counter-examples in negative instances. We compare our tool with the state-of-the-art verification tools for HORS and obtain encouraging results. In contrast to some of the main competition tackling the same problem, our algorithm is fixed-parameter tractable, and we also offer significantly improved performance over the only previously published tool of which we are aware that also enjoys this property. The tool and additional material are available from

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A Saturation Method for Collapsible Pushdown Systems

Cited by 35 publications

References 28 publications

Rewriting Higher-Order Stack Trees

Rewriting Higher-Order Stack Trees

A type-directed abstraction refinement approach to higher-order model checking

C-SHORe

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