The Research Of Synchronic Distance Computation In Petri Nets

Synchronic distance is not only an analyzing metric to describe the dependence relationship between two events, but also a tool to depict dynamic behavior of systems. Computation of synchronic distance involves both structure and initial marking of net systems, which made the solution of synchronic distance become very difficultly undoubtedly. As a result, the algorithm which can get synchronic distance in normal Petri net accurately doesn't have been obtained so far. This thesis makes some studies to the definition of synchronic distance, together with computation of synchronic distance in some subclass of Petri nets and normal Petri nets.The major contributions of this dissertation are as follows:1) By analyzing several typical examples, present definition about synchronic distance existing some shortcomings are pointed out, which is mainly fit for net systems with directed circuit. Therefore modified definition of synchronic distance is further given, which solves all questions asked by preceding typical examples, and explain that the result using modified definition of synchronic distance and adopting observe-place is consistent when solving synchronic distance between transitions. In the end, the relationship between synchronic distance and behavior of net systems is introduced in brief.2) Firstly solution theorem for synchronic distance in marked S-graph is given again according to modified definition of synchronic distance. Secondly this chapter explain that synchronic distance in marked S-net and marked T-net can be directly obtained according to structure of net systems and distributed situation of initial marking, solution theorem of them are given simultaneously. Finally computation of synchronic distance are feasible in these net systems which have the same behavior with marked S-graph and marked T-graph, and simplification steps which keep behavior equivalence are given.3) Using modified definition of synchronic distance, we proof the principle of observe-place by which synchronic distance between transitions is gotten. Pointed out solution of synchronic distance in literature[33] exists shortcoming, which mainly aims at occurrence net. In order to make the range of solution more wide and accurate, concepts of weighted net systems with observe-place and augumented (coverability) tree are introduced in this thesis based on literature[49], at the same time, algorithms for getting matrix about synchronic distance in fair Petri net are presented. In the end, illustrative examples are given. 4) Algorithms for getting synchronic distance between arbitrary two transitions in normal Petri net are discussed at length, and an illustrative example is given.As mentioned above, this thesis makes some studies to synchronic distance in Petri net. These studies have many other problems to discuss, and deserve the further consideration.