Representation Language Of Petri Nets And Reachability Analysis

Reachability is one of the most important properties of Petri nets and its decision problem is also an important topic in Petri nets theories. This thesis analyses the set of reachable markings, and the content is mainly composed of the following aspects:1) Proposes the definition of representation language of Petri nets, and find several Petri nets that have regular representation language.This paper defines a mapping function witch maps a marking to a string, so a Petri net marking is mapped to a string composed by places, and the Petri net's reachable marking set is mapped to the set of the strings called the Petri net's representation language. Obviously a Petri nets usually has more than one representation language.Bounded and fair Petri net both have regular representation language; A Petri net has regular representation language if it has only one primitive repetitive vector.2) Introduces a method to decide the reachability of a Petri net that has regular representation language.This paper proposed the definition of equal representation language. Expand the operation rules of the regular expression, so that a regular expression can be converted to another regular expression that has no nested closure operation in its additional items, and both of the two languages are the same Petri net's representation language. Finally analysis the reachability of the Petri net that has regular representation language.3) Introduces a method to decide whether a Petri net has dead markings.If a Petri net∑1=(N, M0) has dead marking, there are zero marking Petri nets, each of those Petri nets has the same place set with∑1, the union of these Petri nets' reachable marking set DM is the set of dead markings of N, So determining whether the initial marking of∑1 is the member of DM can determining whether∑1 can reach a dead marking.