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arXiv · 1105.1657

Approximating Petri Net Reachability Along Context-free Traces

Mohamed Faouzi Atig·Pierre Ganty
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Abstract

We investigate the problem asking whether the intersection of a context-free language (CFL) and a Petri net language (PNL) is empty. Our contribution to solve this long-standing problem which relates, for instance, to the reachability analysis of recursive programs over unbounded data domain, is to identify a class of CFLs called the finite-index CFLs for which the problem is decidable. The k-index approximation of a CFL can be obtained by discarding all the words that cannot be derived within a budget k on the number of occurrences of non-terminals. A finite-index CFL is thus a CFL which coincides with its k-index approximation for some k. We decide whether the intersection of a finite-index CFL and a PNL is empty by reducing it to the reachability problem of Petri nets with weak inhibitor arcs, a class of systems with infinitely many states for which reachability is known to be decidable. Conversely, we show that the reachability problem for a Petri net with weak inhibitor arcs reduces to the emptiness problem of a finite-index CFL intersected with a PNL.

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Mohamed Faouzi Atig, Pierre Ganty. 2012-01-16. Approximating Petri Net Reachability Along Context-free Traces. https://doi.org/10.4230/lipics.fsttcs.2011.152

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