Two theoretical and practical aspects of knitting technique: Invariants and a new class of Petri net

Document Type

Article

Publication Date

12-1-1997

Abstract

We present two aspects of knitting technique, the structural properties (especially the P- and T-invariants), and the synchronized choice net (a new class of Petri net), that are of both theoretical importance and practical uses to the verification of structural correctness of a Petri net or to detect the structural problem of a Petri net. The unconventional knitting technique has been proved a good approach to synthesize Petri nets with three well-behaved properties, viz., liveness, boundedness, and reversibility, preserved automatically. Hence it can relieve the complexity problem of reachability analysis of Petri net as required by many other methods. This work first proves that the ordinary Petri nets synthesized with knitting technique are structurally bounded, consistent, conservative and safe (when each home place holds one token) using the well-known linear algebra approach. It also provides a procedure for finding P- and T-invariants for Petri net synthesized using the knitting technique. We present examples for P-invariants and show that we can synthesize Petri nets more general than the "asymmetric-choice nets." The aforementioned algorithm for finding P-invariants of ordinary Petri nets is extended to find the P-invariants for a general Petri net synthesized with knitting technique and the arc-ratio rules. We further present a new class of Petri nets, called synchronized choice nets, which are the largest set of Petri nets that can be covered by both T-components and P-components. An algorithm is proposed to find its T-components and the P-components, respectively. The complexity of this algorithm is also presented. The theory of synchronized choice nets has the potential to simplify that for free choice nets. © 1997 IEEE.

Identifier

0031364060 (Scopus)

Publication Title

IEEE Transactions on Systems Man and Cybernetics Part B Cybernetics

External Full Text Location

https://doi.org/10.1109/3477.650057

ISSN

10834419

First Page

962

Last Page

977

Issue

6

Volume

27

Grant

421190

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