Implementing a Matrix Vector Transition Net

Abstract

Aims: Classic Petri nets also known as place transition nets provide many interesting and useful features for system modeling. However they are limited by the place types that are used. An approach is presented where a matrix vector transition net is used for modeling complex system behavior. This is more expressive than a Petri net. Proposed Solution: A modified form of a traditional place transition net is used. The idea is to combine the ideas from Petri net behavior with the matrix vector approach. Implementing the Matrix Vector Transition Net: Ordinary Petri net places are replaced with matrices or vectors. The input and output arcs have a specific function matrix that determines firing. Firing and behavior remains conceptually similar to that of a petri net. Row and column vectors can also be used interchangeably. The behavior of matrix transition nets is similar to that of a place transition net. Instead of tokens, matrix elements are used. This type of structure increases the modeling power, abstraction capacity and the complexity of the net. Case Study: A toy case of an abstract network structure containing processing elements is used to illustrate the use of the matrix vector transition net structure. Results and Findings: The behavior of matrix transition nets is shown to be similar to that of a place transition net. Instead of tokens, matrix elements are used. It is possible to construct a symbolic marking graph or reachability graph for the system This type of structure definitely increases the modeling power, abstraction capacity and the complexity of the net. The matrix transition net could be useful for certain types of communication system problems and complex system interfacing.