Decidable approximations of sets of descendants and sets of normal forms

Genet, Thomas

doi:10.1007/bfb0052368

Cited by 62 publications

(58 citation statements)

References 17 publications

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“…For convenience, we often write → A for → ∆ . Following [10], we formulate Genet's result from [5] as follows: Definition 4. A tree automaton A is compatible with a TRS R if for all state substitutions σ, rules l → r ∈ R and states q ∈ Q, lσ → * A q implies rσ → * A q.…”

Section: Preliminariesmentioning

confidence: 99%

“…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%

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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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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reachability Analysis with State-Compatible Automata

Felgenhauer

Thiemann

2014

Language and Automata Theory and Applications

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“…Given a tree automaton A and a TRS R, the tree automata completion algorithm, proposed in [10,8], computes a tree automaton…”

Section: Approximations Of Reachable Termsmentioning

confidence: 99%

Rewriting Approximations for Fast Prototyping of Static Analyzers

Boichut

Genet

Jensen

et al. 2007

Lecture Notes in Computer Science

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Abstract. This paper shows how to construct static analyzers using tree automata and rewriting techniques. Starting from a term rewriting system representing the operational semantics of the target programming language and given a program to analyze, we automatically construct an over-approximation of the set of reachable terms, i.e. of the program states that can be reached. The approach enables fast prototyping of static analyzers because modifying the analysis simply amounts to changing the set of rewrite rules defining the approximation. A salient feature of this approach is that the approximation is correct by construction and hence does not require an explicit correctness proof. To illustrate the framework proposed here on a realistic programming language we instantiate it with the Java Virtual Machine semantics and perform class analysis on Java bytecode programs.

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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%

“…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%

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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Decidable approximations of sets of descendants and sets of normal forms

Cited by 62 publications

References 17 publications

Reachability Analysis with State-Compatible Automata

Reachability Analysis with State-Compatible Automata

Rewriting Approximations for Fast Prototyping of Static Analyzers

Feasible Trace Reconstruction for Rewriting Approximations

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