Structural Theory Researches Based On Petri Net

Petri nets were the modeling and analyzing tool of nets.Its main characteristic included the fallowing items:parallelism,indefinability,asynchronism,step-by-step described ability and analyzing ability.It could be expressed by figures directly;it also had the profound connotation of mathematics and the foundation.The structural theory researches of Petri nets were main that investigating the distribution and dynamic behavior of Token on some especial structure such as invariant,subnet overcast,siphon(siphon was the compound of spaces:correlative inflow transition must be correlative outflow transition too,so once siphon was not be marked,it would never be marked again.The liveness and feeble liveness of nets were described quite profoundly about this kind of character).The purpose of this thesis was a research in structural theories of Petri nets.The main content of this research was to do a deeper research about the main behavior characteristics of Petri nets by using constitutive analysis theory,simplified technology and Invariable technology and to get some new results.These results as follows.In Petri nets,confusion could bring some trouble for system analysis and system control.The system or model with confusion was not quite good.This thesis included researches about confusion.Basic on three already known confusion (increasing,decreasing and non-increasing and non-decreasing confusion),this thesis had proved that non-increasing non-decreasing confusion was the compound of non-increasing and non-decreasing confusion.Because of this,when the elimination and detection of confusion were being solved,the scale of problems would decrease,at the same time,the necessary and sufficient condition of confusion were gotten from research analysis after,and confusion eliminator created by using the Petri subnets with inhibitor arc,and it also proved that analyzing the constructed confusion eliminator was feasible by using reachability graphs.Current analyzing technology(siphon and traps,siphon and invariant,overcast technology and so on)had to face the problem that exponential order increased along with extending the scale of Petri nets.Petri had proposed the concept of information flows in "'Forgotten Topics' of Net Theory" in 1986.Instead of the original structure,the expression of Petri net which was constructed by using the structural principles of information flows constructed Petri net for the purpose of escaping the problem of spaces explosion.For this purpose,basic on basic net system and C/E system,this thesis had constructed the expression of Petri net of a minimum complete set {P₁,Q} of steam operation.The constructing Petri net described the features of information stream operation and flows simply and accurately.And the compound operation of information flows was reflected by the constructing Petri net.