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Communication Dans Un Congrès Année : 2010

Bounded Underapproximations

Résumé

We show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L' included in L which has the same Parikh (commutative) image as L. Bounded languages, introduced by Ginsburg and Spanier, are subsets of regular languages of the form w1*w2*...wk* for some finite words w1,...,wk. In particular bounded subsets of context-free languages have nice structural and decidability properties. Our proof proceeds in two parts. First, using Newton's iterations on the language semiring, we construct a context-free subset Ls of L that can be represented as a sequence of substitutions on a linear language and has the same Parikh image as L. Second, we inductively construct a Parikh-equivalent bounded context-free subset of Ls. We show two applications of this result in model checking: to underapproximate the reachable state space of multithreaded procedural programs and to underapproximate the reachable state space of recursive counter programs. The bounded language constructed above provides a decidable underapproximation for the original problems. By iterating the construction, we get a semi-algorithm for the original problems that constructs a sequence of underapproximations such that no two underapproximations of the sequence can be compared. This provides a progress guarantee: every word w in L is in some underapproximation of the sequence. In addition, we show that our approach subsumes context-bounded reachability for multithreaded programs.
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Dates et versions

hal-00608175 , version 1 (12-07-2011)

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Pierre Ganty, Rupak Majumdar, Benjamin Monmege. Bounded Underapproximations. Proceedings of the 22nd International Conference on Computer Aided Verification (CAV'10), Jul 2010, Edinburgh, United Kingdom. pp.600-614, ⟨10.1007/978-3-642-14295-6_52⟩. ⟨hal-00608175⟩
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