The Reachability Problem for Vector Addition System with One Zero-Test

We consider here a variation of Vector Addition Systems where one counter can be tested for zero, extending the reachability proof by Leroux for Vector Addition System to our model. This provides an alternate, and hopefully simpler to understand, proof of the reachability problem that was originally proved by Reinhardt.

[1]  Mohamed Faouzi Atig,et al.  Approximating Petri Net Reachability Along Context-free Traces , 2011, FSTTCS.

[2]  Jérôme Leroux Vector Addition System Reversible Reachability Problem , 2011, CONCUR.

[3]  Parosh Aziz Abdulla,et al.  General decidability theorems for infinite-state systems , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[4]  Klaus Reinhardt,et al.  Reachability in Petri Nets with Inhibitor Arcs , 2008, RP.

[5]  Jérôme Leroux,et al.  Vector addition system reachability problem: a short self-contained proof , 2011, POPL '11.

[6]  Parosh Aziz Abdulla,et al.  Minimal Cost Reachability/Coverability in Priced Timed Petri Nets , 2009, FoSSaCS.

[7]  S. Rao Kosaraju,et al.  Decidability of reachability in vector addition systems (Preliminary Version) , 1982, STOC '82.

[8]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

[9]  Alain Finkel,et al.  Place-Boundedness for Vector Addition Systems with one zero-test , 2010, FSTTCS.

[10]  Alain Finkel,et al.  Mixing Coverability and Reachability to Analyze VASS with One Zero-Test , 2010, SOFSEM.

[11]  Bernhard Rumpe,et al.  SOFSEM 2010: Theory and Practice of Computer Science, 36th Conference on Current Trends in Theory and Practice of Computer Science, Spindleruv Mlýn, Czech Republic, January 23-29, 2010. Proceedings , 2010, SOFSEM.

[12]  Jérôme Leroux The General Vector Addition System Reachability Problem by Presburger Inductive Invariants , 2009, 2009 24th Annual IEEE Symposium on Logic In Computer Science.

[13]  Jean-Luc Lambert,et al.  A Structure to Decide Reachability in Petri Nets , 1992, Theor. Comput. Sci..

[14]  Ernst W. Mayr An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..