Polynomial time decidability of monotone liveness of time bounded AC/DC nets
Petri net is a mathematical model for concurrent systems. Liveness is one of important properties of Petri net. Liveness problem of general Petri net is of exponential space complexity and subclasses are suggested with less computational complexity. It is well known that liveness problem of bounded (extended) free choice net its solved in deterministic polynomial time. This paper treats liveness problem of AC/DC nets. AC/DC net is a subclass of Petri net that exhibits no confusion (mixture of concurrency and conflict). This class properly includes the class of free choice nets. It is shown that every minimal siphon of an AC/DC net is trap if and only if every strongly connected siphon is a trap. This result shows that monotone liveness of bounded AC/DC net is solved in deterministic polynomial time. It is shown that this result is true of bounded time AC/DC net with static fair condition.
liveness petri net concurrent system computational complexity