NDLI: Presburger Vector Addition Systems

Content Provider	IEEE Xplore Digital Library
Author	Leroux, J.
Copyright Year	2013
Description	Author affiliation: LaBRI, Univ. of Bordeaux, Talence, France (Leroux, J.)
Abstract	The reachability problem for Vector Addition Systems (VAS) is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reachability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immediate. However, in this case, the computation of a Presburger formula denoting the reachability set is an open problem. In this paper we close this problem by proving that if the reachability set of a VAS is definable in the Presburger arithmetic, then the VAS is flatable, i.e. its reachability set can be obtained by runs labeled by words in a bounded language. As a direct consequence, classical algorithms based on acceleration techniques effectively compute a formula in the Presburger arithmetic denoting the reachability set.
Starting Page	23
Ending Page	32
File Size	344196
Page Count	10
File Format	PDF
ISBN	9781479904136
ISSN	10436871
DOI	10.1109/LICS.2013.7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-06-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Vectors Acceleration Lattices TV Petri nets Complexity theory Reachability Infinite State Systems flatability Presburger Vector Addition Systems
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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