Bonnet, Rémi and FInkel, Alain and Leroux, Jérôme and Zeitoun, Marc - Model Checking Vector Addition Systems with one zero-test

lmcs:870 - Logical Methods in Computer Science, June 19, 2012, Volume 8, Issue 2
Model Checking Vector Addition Systems with one zero-test

Authors: Bonnet, Rémi and FInkel, Alain and Leroux, Jérôme and Zeitoun, Marc

We design a variation of the Karp-Miller algorithm to compute, in a forward manner, a finite representation of the cover (i.e., the downward closure of the reachability set) of a vector addition system with one zero-test. This algorithm yields decision procedures for several problems for these systems, open until now, such as place-boundedness or LTL model-checking. The proof techniques to handle the zero-test are based on two new notions of cover: the refined and the filtered cover. The refined cover is a hybrid between the reachability set and the classical cover. It inherits properties of the reachability set: equality of two refined covers is undecidable, even for usual Vector Addition Systems (with no zero-test), but the refined cover of a Vector Addition System is a recursive set. The second notion of cover, called the filtered cover, is the central tool of our algorithms. It inherits properties of the classical cover, and in particular, one can effectively compute a finite representation of this set, even for Vector Addition Systems with one zero-test.


Source : oai:arXiv.org:1205.4458
DOI : 10.2168/LMCS-8(2:11)2012
Volume: Volume 8, Issue 2
Published on: June 19, 2012
Submitted on: October 7, 2011
Keywords: Computer Science - Discrete Mathematics,Computer Science - Formal Languages and Automata Theory,F.1.1


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