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Concurrency: a relational approach

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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.