Vector Addition System Reversible Reachability Problem
The reachability problem for vector addition systems is a central problem of net theory. This problem is known to be decidable but the complexity is still unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds complexity are known. In this paper we consider the reversible reachability problem. This problem consists to decide if two configurations are reachable one from each other. We show that this problem is EXPSPACE-complete. As an application of the introduced materials we characterize the reversibility domains of a vector addition system.
KeywordsCoverability Problem Simple Cycle Total Cycle Reachability Problem Projected Component
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- [BF97]Bouziane, Z., Finkel, A.: Cyclic petri net reachability sets are semi-linear effectively constructible. Electr. Notes Theor. Comput. Sci. 9 (1997)Google Scholar
- [CLM76]Cardoza, E., Lipton, R.J., Meyer, A.R.: Exponential space complete problems for petri nets and commutative semigroups: Preliminary report. In: STOC 1976, pp. 50–54. ACM, New York (1976)Google Scholar
- [Hau90]Hauschildt, D.: Semilinearity of the Reachability Set is Decidable for Petri Nets. PhD thesis, University of Hamburg (1990)Google Scholar
- [Ler11]Leroux, J.: Vector addition system reachability problem: a short self-contained proof. In: Ball, T., Sagiv, M. (eds.) Proceedings of the 38th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2011, Austin, TX, USA, January 26-28, pp. 307–316. ACM, New York (2011)Google Scholar
- [May81]Mayr, E.W.: An algorithm for the general petri net reachability problem. In: Conference Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computation, STOC 1981, Milwaukee, Wisconsin, USA, May 11-13, pp. 238–246. ACM, New York (1981)Google Scholar
- [Rac78]Rackoff, C.: The covering and boundedness problems for vector addition systems. Theoretical Computer Science 6(2) (1978)Google Scholar
- [ST77]Sacerdote, G.S., Tenney, R.L.: The decidability of the reachability problem for vector addition systems (preliminary version). In: Conference Record of the Ninth Annual ACM Symposium on Theory of Computing, Boulder, Colorado, USA, May 2-4, pp. 61–76. ACM, New York (1977)Google Scholar