Equational Abstraction Refinement for Certified Tree Regular Model Checking

Boichut, Yohan; Boyer, Benoît; Genet, Thomas; Legay, Axel

doi:10.1007/978-3-642-34281-3_22

Cited by 7 publications

(13 citation statements)

References 32 publications

(39 reference statements)

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“…Using the sticking-out graph, he proposed an algorithm detecting simple loops in TRS application and infering equations of We have to investigate this further and see if it can, in practice, infer equations precise enough to prove the examples of Section 6.6. Note that, it is also possible to refine equations automatically using Counter Example Guided Abstraction Refinement (CEGAR) completion algorithm [44]. This provides a nice alternative to equation inference.…”

Section: Discussionmentioning

confidence: 99%

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Termination criteria for tree automata completion

Genet

2016

Journal of Logical and Algebraic Methods in Programming

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This paper presents two criteria for the termination of tree automata completion. Tree automata completion is a technique for computing a tree automaton recognizing or over-approximating the set of terms reachable w.r.t. a term rewriting system. The first criterion is based on the structure of the term rewriting system itself. We prove that for most of the known classes of linear rewriting systems preserving regularity, the tree automata completion is terminating. Moreover, it outputs a tree automaton recognizing exactly the set of reachable terms. When the term rewriting system is outside of such classes, the set of reachable terms can be approximated using a set of equations defining an abstraction. The second criterion, which holds for any left-linear term rewriting system, defines sufficient restrictions on the set of equations for the tree automata completion to terminate. We then show how to take advantage of this second criterion to use completion as a new static analysis technique for functional programs. Some examples are demonstrated using the Timbuk completion tool.

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Section: Discussionmentioning

confidence: 99%

“…Finally, the verification mechanisms of [41] use automatic abstraction refinement: when the approximation is too coarse it is automatically refined. This can be also performed in the completion setting [44] and adapted to the analysis of functional programs using completion [43].…”

Section: Related Workmentioning

confidence: 99%

Termination criteria for tree automata completion

Genet

2016

Journal of Logical and Algebraic Methods in Programming

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“…Besides, the verification mechanisms of [22] use automatic abstraction refinement. This can be also performed in the completion setting [3] and adapted to the analysis of functional programs [15]. Finally, using a simpler (first order) formalism, i.e.…”

Section: Related Workmentioning

confidence: 99%

“…In practice, checking if CP (R, A k R,E ) = ∅ is sufficient to know that A k R,E is a fixpoint. However, a fixpoint cannot always be finitely reached 3 . To ensure termination, one can provide a set of approximating equations to overcome infinite rewriting and completion divergence.…”

Section: The Full Completion Algorithmmentioning

confidence: 99%

Towards Static Analysis of Functional Programs Using Tree Automata Completion

Genet

2014

Rewriting Logic and Its Applications

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International audienceThis paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for com-puting or approximating the set of terms reachable by a rewriting rela-tion. The completion algorithm we focus on is parameterized by a set E of equations controlling the precision of the approximation and influenc-ing its termination. For completion to be used as a static analysis, the first step is to guarantee its termination. In this work, we thus give a sufficient condition on E and T (F) for completion algorithm to always terminate. In the particular setting of functional programs, this condi-tion can be relaxed into a condition on E and T (C) (terms built on the set of constructors) that is closer to what is done in the field of static analysis, where abstractions are performed on data

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“…= ∅ is a well-known undecidable problem, where I is an initial set of terms, Bad is a set of forbidden terms and R * (I) denotes the terms issued from I using the rewrite system R. Some techniques compute regular over-approximations of R * (I) in order to show that no term of Bad is reachable from I [7,6,1,4].…”

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confidence: 99%