Selected publications at LSV

Abstract:
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'⊆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*... wm* for some w1,...,wm∈ Σ*. In particular bounded context-free languages have nice structural and decidability properties. Our proof proceeds in two parts. First, we give a new construction that shows that each context free language L has a subset LN that has the same Parikh image as L and that can be represented as a sequence of substitutions on a linear language. Second, we inductively construct a Parikh-equivalent bounded context-free subset of LN.
    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∈L is in some underapproximation of the sequence, and hence, a program bug is guaranteed to be found. In particular, we show that verification with bounded languages generalizes context-bounded reachability for multithreaded programs.

@article{GMM-fmsd2012,
   author = {Ganty, Pierre and Majumdar, Rupak and Monmege, Benjamin},
   DOI = {10.1007/s10703-011-0136-y},
   journal = {Formal Methods in System Design},
   month = apr,
   number = {2},
   pages = {206-231},
   publisher = {Springer},
   title = {Bounded underapproximations},
   url = {http://www.lsv.ens-cachan.fr/Publis/PAPERS/PDF/GMM-fmsd12.pdf},
   volume = {40},
   year = {2012},
}

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