Concorrência, redes de petri e teoria da informação: aspectos comuns.

Abstract

Information theory is a successfully discipline concerning point-to-point systems but many problems in networked communication systems remain open as for example the capacity region of some multi-user channels are unknown. Considering the very basic fact that trasmission of information from a source point to a destination point is due by choosing physical events on the transmitter side in order to cause physical events on the receiver side, it is observed that in case of networked systems in general it is impossible to obtain a total ordering of such that events. In other hand lack of ordering of events in distributed systems was explored by Carl A. Petri that has introduced the precise notion of "concurrency" between events in the circle of the computer science. The today well known Petri nets efficiently model aspects os concurrence and causality between events. In view of comments above i t is natural ask about relationship between problems of capacity of networked communication systems and modelling of concurrent systems. This is the main motivation of this thesis. In this thesis it started the use of Petri nets in the analysis of the capacity of multipoint systems. To this end, a previous defined measure of complexity of Petri nets named compressibility is extended. It is shown that the compressibility of a Petri net can obtained from an adjacency matrix associated with its coverability graph. Some of the properties of this measure are presented. From compressibility definition, some conclusions related to the representation and the behavior of concurrent systems are presented. Examples of concurrent noiseless systems generating sequences of symbols that obey some constraints similar to those found in magnetic recording systems. I t is shown how to calculate the capacity of such that systems by means Petri nets modelling and a handy labeling function that associates physical events to information.