Time causal processes in time Petri nets with weak semantics

In this paper, we present a method for state space reduction of dense-time Petri nets (TPNs) – an extension of Petri nets by adding a time interval to every transition for its firing. The time elapsing and memory operating policies define different semantics for TPNs. The decidability of many standard problems in the context of TPNs depends on the choice of their semantics. The state space of the TPN is infinite and non-discrete, in general, and, therefore, the analysis of its behavior is rather complicated. To cope with the problem, we elaborate a state space discretization technique and develop a partial order semantics for TPNs equipped with weak time elapsing and intermediate memory policies.