The Research Of Confluence Property And Home State Of Petri Nets

Confluence property and home state are two important properties of Petri nets. They have important roles and values in the application fields. However, in pure Petri nets theory, research work on the confluence property and home state of Petri nets is very little. So in this thesis, we make some studies about confluence property and home state of Petri nets.The major contributions of this dissertation are as follows:1. Start off with simple subclasses, what kinds of Petri nets have confluence property is studied. Subclasses of Petri nets as live marked S-graph, live marked T-graph, bounded conflict-free Petri nets, bounded marked T-graph (T-net), marked T-graph without source transitions, live and bounded marked free-choice Petri nets are discussed in succession, and they are all proved to possess confluence property.2. The confluence property of net systems which have the same behavior with above-mentioned special subclasses is discussed. A simplification method which keeps behavior equivalence is given, since to determine whether or not two net systems equivalent is very complex. By this way, to judge whether a given net system has the same behavior with the aforementioned special subclasses of Petri nets becomes relatively simple. If the given net system has the same behavior with some special subclass, whether it possesses confluence property can be determined very easily.3. The preservation problems for confluence property in synchronous and sharing synthesis of net systems are discussed. Some combination methods are proved to preserve the confluence property, such as synchronous synthesis with live subsystems, synchronous synthesis which remains complete behavior invariance, S-composition, sharing synthesis with live subsystems which preserve liveness and so on. At the same time for sharing synthesis expansions are made and broader conclusions are proposed.4. On the basis of the research work on confluence property of Petri nets, the property of home state is discussed. Some subclasses of Petri nets are pointed out to contain home states. A preliminary discussion on characteristics of home states in live and baounded net systems is made, and the relationships between traps and home states are discussed.