Modeling And Analyzing Reversible Gates And Reversible Circuits Based On Petri Net

Petri net is widely known as a useful tool for modeling and analyzing the discrete and parallel systems. The initial purpose of designing Petri net is to model and analyze asynchronous and concurrent computing models. There are two forms of Petri net:graphic and mathematic ones. The development of Petri net has provided a richful theoretical basis for computer science. It has been widely used in the computer science, distributed computation and modeling the concurrent computing systems. The theory of Petri net is considered as a kind of automatical theory.In this thesis, Petri net is used in modeling the reversible gates and reversible circuits. Firstly, inspired from the Petri net models of logic gates, such as AND and OR, we design the Petri net models of Fredkin gate, and then we analyze its reachability, aliveness, boundary, structural boundary, dead lock and concurrentary. By transferring the Petri net model of the Fredkin gate into mathematical forms, we can easily analyze the Petri net models. We get the following results:the Petri net of the Fredkin gate is structural bounded, and there is no deadlocks, traps and conflicts. And there are two couples of concurrent transitions. But the Petri net is not alive.Reversible gates and ciucuits are the hot researching fields of Quantum computing. The reversible circuits consist of Fredkin reversible gates. Based on the models of Petri net of Fredkin gate, we have also modeled the reversible circuit by Petri net. Most of the properties of Fredkin gate such as aliveness, boundedness and so on are still useful in the reversible circuit. Some properties of the reversible circuit are not in the Fredkin gate, three of them are considered, and they are deadlock, reachability and aliveness.