Petri net synthesis and synchronization using knitting technique

Abstract

Petri net (PN) synthesis can avoid the state exploration problem, which is of exponential complexity, by guaranteeing the correctness in the Petri net while incrementally expanding the net. The conventional Petri net synthesis approaches, in general, suffer the drawback of only being able to synthesize a few classes of nets. However, the knitting technique, originally proposed by Chao [1-4], can synthesize Petri nets beyond assymetricchoice nets. In addition, one major advantage of the knitting technique is that the resultant Petri net is guaranteed to be live, bounded, and reversible -the well-behaved properties. Therefore, the cumbersome reanalysis and modification procedures that are inevitable for the conventional Petri net synthesis methods can be avoided. Most current synthesis techniques cannot handle systems with shared resources. Zhou et al. [5] presented the conditions for a PN containing Sequential Mutual Exclusion (SME) to be live, bounded, and deadlock-free. The major motivation of this work is to generalize Zho et al.'s pioneering work [5] and to extend the knitting technique to construction of classes of PNs that involve synchronization and shared resources according to the synthesis rules. In addition, the knitting technique developed prior to this work concentrated on the structural relationships among the pseudo-processes only and was not related to the marking. This paper is the first work to consider marking in the PN synthesis with the knitting technique.

Extended Synchronized Choice Nets

“…If we consider each PT-handle in this Z P to be a process, then the processes (called SMEs) in the Z P are mutually sequentialized (originally mutually exclusive) [8] as mentioned in Section 1. Note that there are three SMEs in series in Figure 2; such a structure was not considered in [8,16].…”

“…Tokens in places with negative y values cause tokens in D to be drained out by firing some t d (see Figure 2). Note that all output transitions of a p d in D must be synchronized by a circuit c [16]. All places in c are in an S-invariant.…”

Extending knitting algorithm to synthesize resource sharing FMS

“…New paths are added from ng to nj according to two guidelines: (1) do not disturb the reachable markings of the old net and (2) ensure that the new path is live, bounded, and reversible. Each new path is defined as PSP, where every node (except its two end nodes) has a single input and a single output place.…”

“…The synthesized nets, however, are limited in classes because some generations are prohibited [2]. For instance, there are no ordering of firings among a set of transitions that are exclusive to each other.…”

Knitting technique with TP-PT generations for Petri net synthesis

“…Therefore, it is desired to have a synthesis approach which provides a set of guidelines for the designer to build a PN. Various synthesis approaches have been proposed: top-down/ bottom-up [8,10,15], peer entity generation [14], and knitting [3][4][5][6][7].…”