Polynomial Time Solvability of Liveness Problem of Siphon Containing Circuit Nets

Petri net is an effective modeling tool for concurrent systems. Liveness problem is one of analysis problems in Petri net theory verifying whether the system is free from any local deadlocks. It is well known that computational complexity of liveness problem of general Petri net is deterministic exponential space. Some subclasses, such as marked graph and free choice net, are suggested where liveness problem is verified in less complexity. This paper studies liveness of siphon containing circuit (SCC) net. Liveness condition based on algebraic inequalities is shown. Then polynomial time decidability of liveness of SCC net is derived, if the given net is known to be an SCC net a priori.