A synthesis technique of general petri nets

Abstract

Abstract. The general Petri net (GPN) is useful for modeling flexible manufacturing systems with multiple robots and workstations [15] and for parallel programs [8]. A problem of using reachability analysis for analyzing Petri nets (PN) is the large number of states generated. Most of the existing synthesis techniques do not deal with GPN. Koh et al. [15] invented a synthesis technique for GPN. We propose to improve their achievement by adding the simple Arc-ratio rules to Yaw's knitting technique [37,38,39] based on the notion of structure relationship together with new path generations, which mark the most distinct feature compared with other approaches. The synthesis rules and procedures of how to update the temporal matrix and structure synchronic distance are presented. The Arc-ratio rules for GPN are also presented. One can successfully synthesize complicated Petri nets using these rules. An example to synthesize a Petri net in [15] is illustrated. The correctness of each synthesis rule with an appropriate Arc-ratio rule for GPN is proved.

Petri net synthesis and synchronization using knitting technique

“…In [9], the corresponding net obtained is called its reverse-dual, N rd . These rules have been proved in [8] to satisfy the two guidelines. To save space, we will not duplicate it here.…”

“…To save space, we will present Rules TT.2, TT.3, TT.4, and PP.2. For other rules, the reader is can refer to [8].…”

“…It can synthesize protocols [1] among multiple parties and has been applied to synthesis of communication protocols and automated manufacturing systems [7]. In [8], we extended these rules to synthesize General Petri Nets (GPNs) whose arcs have multiple weights. This technique can synthesize nets more generally than can free-choice (FC) *1 , extended free-choice (EFC) *2 or assymetricchoice nets (AC) *3 [MUR 89a].…”

Knitting technique with TP-PT generations for Petri net synthesis

“…For more details and examples, please refer to [4,7]. Definition 3 A home place p h is defined as an input place of a t α where t α is enabled in the initial marking of a PN.…”

“…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].…”