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, or equivalently if they are in the same strongly connected component of the reachability graph. 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.

• 68Q17 - Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
• 68Q85 - Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)