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On minimal elements of upward-closed sets
- Source :
-
Theoretical Computer Science . May2009, Vol. 410 Issue 24/25, p2442-2452. 11p. - Publication Year :
- 2009
-
Abstract
- Abstract: Upward-closed sets of integer vectors enjoy the merit of having a finite number of minimal elements, which is behind the decidability of a number of Petri net related problems. In general, however, such a finite set of minimal elements may not be effectively computable. In this paper, we develop a unified strategy for computing the sizes of the minimal elements of certain upward-closed sets associated with Petri nets. Our approach can be regarded as a refinement of a previous work by Valk and Jantzen (in which a necessary and sufficient condition for effective computability of the set was given), in the sense that complexity bounds now become available provided that a bound can be placed on the size of a witness for a key query. The sizes of several upward-closed sets that arise in the theory of Petri nets as well as in backward-reachability analysis in automated verification are derived in this paper, improving upon previous decidability results shown in the literature. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03043975
- Volume :
- 410
- Issue :
- 24/25
- Database :
- Academic Search Index
- Journal :
- Theoretical Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 39354110
- Full Text :
- https://doi.org/10.1016/j.tcs.2009.02.036