Reachability Analysis over Term Rewriting Systems

Feuillade, Guillaume; Genet, Thomas; Tông, Valérie Viêt Triêm

doi:10.1007/s10817-004-6246-0

Cited by 62 publications

(124 citation statements)

References 28 publications

(48 reference statements)

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“…Given a tree automaton A and a TRS R, the tree automata completion algorithm, proposed in [Gen98,FGVTT04], computes a tree automaton A k such that L(A k ) = R * (L(A)) when it is possible (for the classes of TRSs covered by this algorithm see [FGVTT04]) and such that L(…”

Section: Tree Automata Completionmentioning

confidence: 99%

“…[FGVTT04]). To build A i+1 from A i , we achieve a completion step which consists in finding critical pairs between → R and → A i .…”

Section: Tree Automata Completionmentioning

confidence: 99%

“…This problem, which can easily be solved on strongly terminating TRS (by rewriting s into all its possible reduced forms and compare them to t), is undecidable on non terminating TRS. There exists several syntactic classes of TRSs for which this problem becomes decidable: some are surveyed in [FGVTT04], more recent ones are [GV98,TKS00]. In general, the decision procedures for those classes compute a finite tree automaton recognizing the possibly infinite set of terms reachable from a set E ⊆ T (F) of initial term, by R, denoted by R * (E).…”

Section: Introductionmentioning

confidence: 99%

“…Then, provided that s ∈ E, those procedures check whether t ∈ R * (E) or not. On the other hand, outside of those decidable classes, one can prove s → * R t using over-approximations of R * (E) [Jac96,Gen98,FGVTT04] and proving that t does not belong to this approximation.…”

Section: Introductionmentioning

confidence: 99%

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Feasible Trace Reconstruction for Rewriting Approximations

Boichut¹,

Genet

2006

Lecture Notes in Computer Science

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Abstract. Term Rewriting Systems are now commonly used as a modeling language for programs or systems. On those rewriting based models, reachability analysis, i.e. proving or disproving that a given term is reachable from a set of input terms, provides an efficient verification technique. For disproving reachability (i.e. proving non reachability of a term) on non terminating and non confluent rewriting models, KnuthBendix completion and other usual rewriting techniques do not apply. Using the tree automaton completion technique, it has been shown that the non reachability of a term t can be shown by computing an overapproximation of the set of reachable terms and prove that t is not in the approximation. However, when the term t is in the approximation, nothing can be said. In this paper, we refine this approach and propose a method taking advantage of the approximation to compute a rewriting path to the reachable term when it exists, i.e. produce a counter example. The algorithm has been prototyped in the Timbuk tool. We present some experiments with this prototype showing the interest of such an approach w.r.t. verification of rewriting models.

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Section: Tree Automata Completionmentioning

confidence: 99%

“…[FGVTT04]). To build A i+1 from A i , we achieve a completion step which consists in finding critical pairs between → R and → A i .…”

Section: Tree Automata Completionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Feasible Trace Reconstruction for Rewriting Approximations

Boichut¹,

Genet

2006

Lecture Notes in Computer Science

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“…Tree automata completion, conceived by Genet et al [4,5], is based on the stronger requirements that L 0 ⊆ L and L is itself closed under rewriting, i.e., R(L) ⊆ L. This is accomplished by constructing L as the language accepted by a bottom-up tree automaton A that is compatible with R: Whenever lσ is accepted in state q by A, where l → r ∈ R and σ maps variables to states of A, we demand that rσ is also accepted in q. If A is deterministic or if R is a left-linear term rewrite system, then compatibility ensures that L(A) is closed under rewriting by R. Example 1.…”

Section: Introductionmentioning

confidence: 99%

Reachability Analysis with State-Compatible Automata

Felgenhauer

Thiemann

2014

Language and Automata Theory and Applications

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Abstract. Regular tree languages are a popular device for reachability analysis over term rewrite systems, with many applications like analysis of cryptographic protocols, or confluence and termination analysis. At the heart of this approach lies tree automata completion, first introduced by Genet for left-linear rewrite systems. Korp and Middeldorp introduced so-called quasi-deterministic automata to extend the technique to nonleft-linear systems. In this paper, we introduce the simpler notion of state-compatible automata, which are slightly more general than quasideterministic, compatible automata. This notion also allows us to decide whether a regular tree language is closed under rewriting, a problem which was not known to be decidable before. Several of our results have been formalized in the theorem prover Isabelle/HOL. This allows to certify automatically generated non-confluence and termination proofs that are using tree automata techniques.

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Effective strategic programming for Java developers

2012

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SUMMARYIn object programming languages, the Visitor design pattern allows separation of algorithms and data structures. When applying this pattern to tree‐like structures, programmers are always confronted with the difficulty of making their code evolve. One reason is that the code implementing the algorithm is interwound with the code implementing the traversal inside the visitor. When implementing algorithms such as data analyses or transformations, encoding the traversal directly into the algorithm turns out to be cumbersome as this type of algorithm only focuses on a small part of the data‐structure model (e.g., program optimization). Unfortunately, typed programming languages like Java do not offer simple solutions for expressing generic traversals. Rewrite‐based languages like ELAN or Stratego have introduced the notion of strategies to express both generic traversal and rule application control in a declarative way. Starting from this approach, our goal was to make the notion of strategic programming available in a widely used language such as Java and thus to offer generic traversals in typed Java structures. In this paper, we present the strategy language SL that provides programming support for strategies in Java. Copyright © 2012 John Wiley & Sons, Ltd.

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Reachability Analysis over Term Rewriting Systems

Cited by 62 publications

References 28 publications

Feasible Trace Reconstruction for Rewriting Approximations

Feasible Trace Reconstruction for Rewriting Approximations

Reachability Analysis with State-Compatible Automata

Effective strategic programming for Java developers

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