We investigate the problem asking whether the intersection of a context-free language (CFL) and a Petri net language (PNL) (with reachability as acceptance condition) 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.
@InProceedings{atig_et_al:LIPIcs.FSTTCS.2011.152, author = {Atig, Mohamed Faouzi and Ganty, Pierre}, title = {{Approximating Petri Net Reachability Along Context-free Traces}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)}, pages = {152--163}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-34-7}, ISSN = {1868-8969}, year = {2011}, volume = {13}, editor = {Chakraborty, Supratik and Kumar, Amit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.152}, URN = {urn:nbn:de:0030-drops-33448}, doi = {10.4230/LIPIcs.FSTTCS.2011.152}, annote = {Keywords: Petri nets, Context-free Grammars, Reachability Problem} }
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