Synchronized Tree Languages for Reachability in Non-right-linear Term Rewrite Systems

Boichut, Yohan; Pelletier, Vivien; Réty, Pierre

doi:10.1007/978-3-319-44802-2_4

Cited by 1 publication

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“…Comparison with [1,2,3,4,5]: If no input arguments are used, this paper is equivalent to [2], which actually also needed the rewrite system to be leftand-right linear (the erratum of [2] is given in [12]), due to the semantics of logic programs. An extension of [2] to deal with non right-linear rewrite system is proposed in [13].…”

Section: Introductionmentioning

confidence: 99%

Towards More Precise Rewriting Approximations

Boichut

Chabin

Réty

2015

Language and Automata Theory and Applications

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To check a system, some verification techniques consider a set of terms I that represents the initial configurations of the system, and a rewrite system R that represents the system behavior. To check that no undesirable configuration is reached, they compute an over-approximation of the set of descendants (successors) issued from I by R, expressed by a tree language. Their success highly depends on the quality of the approximation. Some techniques have been presented using regular tree languages, and more recently using non-regular languages to get better approximations: using context-free tree languages [1] on the one hand, using synchronized tree languages [2] on the other hand. In this paper, we merge these two approaches to get even better approximations: we compute an over-approximation of the descendants, using synchronized-contextfree tree languages expressed by logic programs. We give several examples for which our procedure computes the descendants in an exact way, whereas the former techniques compute a strict over-approximation.

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