A note on transition systems

This paper introduces a mathematical structure called transition systems. The notion of transition systems has been developed as a result of the study of Petri nets and vector addition systems. The intended use of transition systems is to model concurrent and asynchronous events. The concept of information flow in a complex system and communication between parts of a complex system can be formulated in this formal structure. This paper is concerned with the mathematical properties rather than the applications of transition systems. Patterns of activities in complex systems are defined in terms of termination and finiteness properties of transition systems. Concepts of conservation and repetitivity have been introduced. Structural properties of restricted classes of transition systems have been studied.