Depth-First Net Unfoldings and Equivalent Reduction

Abstract

In Petri net unfolding, according to the strategies of breadth first and depth first, the biggest problem lies in the potential explosion of the state space. Unfolding generates either accessible trees or branch processes. Making marking reduction or branch cutting accessible proves to be an effective approach to mitigating the state space expansion. In this paper, we propose three reduction rules based on similarity equivalence, conduct state space reduction, present three theorems supported by a case study, and propose a new unfolding algorithm for the unfolding process. In both the new case and the experiments, the completeness, optimality, completeness, and memory and time consumption are reduced by about 60%.

Improved Design of Concurrent Synchronization System Controller Based on Petri Net

“…According to the literature [9], the finite termination and correctness of the Petri net reachability tree generation algorithm are performed. Combining the same identification nodes in the reachability tree, the reachability graph algorithm [10][11][12] ensures the limited termination and correctness of the reachability graph generation algorithm.…”

“…According to the state equation of the net theory [10][11][12], it is known that M c −stack(top) = A T t, where A T represents the transferred array of the correlation/incidence matrix [9] of the net C. t = f ((stack(top), M c )). Thus, from every two nodes of the RMG (C) and their associated edges, the previous equation of state is used to obtain the net (P c , T c , F c ).…”

“…The synchronization of the concurrent events [8,9] is to execute a pair of critical areas protected by lock synchronization sequentially twice. Through deadlock avoidance [10,11] and deadlock elimination, the deadlock is removed from the root. Thus, further deadlock is prevented.…”