Concurrency: a relational approach



Dr. Ridha Khedri

and

Dr. Jules Desharnais


Abstract

We model processes by means of a mathematical entity that we call a relational process. This model describes a process as an open system from which the description of the process as a closed system can be easily obtained. Also, it represents not only the actions of the process but also the resources needed to accomplish its behaviour. Using this model, we first define two operators. Each of these represents an extreme perception of concurrency. One, the interleaved parallel composition operator, reduces concurrency to interleaving and the other, the maximal totally synchronous parallel composition operator, reduces concurrency to a totally synchronous behaviour. Second, by combining these operators, we define the maximal true-concurrency composition operator, which is an operator expressing true concurrency. When many processes interfere on the same resource in order to modify it, each in its way, the two maximal operators express this situation by letting the final value of the variable modelling this resource be indeterminate. So, they allow the detection of interferences between processes. We present some of the properties of these operators.