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**Comportements de processus.**
*(English)*
Zbl 0538.68062

Les mathématiques de l’informatique, AFCET Colloq., Paris 1982, 35-68 (1982).

[For the entire collection see Zbl 0507.00016.]

The paper deals with the semantics of processes and of synchronized nets of processes. The semantics of a process p is defind by a triple of languages \(L^{init}(p)\), \(L^{fin}(p)\), \(L^{\inf}(p)\) which represent the initial, the finite successful and the infinite behaviours of p, respectively. Many properties of processes are expressed in terms of the relations among these languages. The most important of these properties are normality (every initial behaviour can be extended to a finite successful one) and centrality (every initial behaviour can be extended to an infinite one). The languages are recognized by non- deterministic automata enriched to deal with infinite words. In particular the authors study rational processes, i.e. those having as semantics an infinite language which is recognizable by a finite automaton. The composition of processes is then studied. The behaviour of a synchronized net of processes is obtained by constraining the behaviours of its components through a synchronization condition, expressible itself as a process. Many properties of synchronized nets of processes are studied, which are expressed in terms of the properties of the components. Finally, the authors introduce two notions of control of a net, by giving the definitions of centralized and distributed control, and analyze their properties.

The paper deals with the semantics of processes and of synchronized nets of processes. The semantics of a process p is defind by a triple of languages \(L^{init}(p)\), \(L^{fin}(p)\), \(L^{\inf}(p)\) which represent the initial, the finite successful and the infinite behaviours of p, respectively. Many properties of processes are expressed in terms of the relations among these languages. The most important of these properties are normality (every initial behaviour can be extended to a finite successful one) and centrality (every initial behaviour can be extended to an infinite one). The languages are recognized by non- deterministic automata enriched to deal with infinite words. In particular the authors study rational processes, i.e. those having as semantics an infinite language which is recognizable by a finite automaton. The composition of processes is then studied. The behaviour of a synchronized net of processes is obtained by constraining the behaviours of its components through a synchronization condition, expressible itself as a process. Many properties of synchronized nets of processes are studied, which are expressed in terms of the properties of the components. Finally, the authors introduce two notions of control of a net, by giving the definitions of centralized and distributed control, and analyze their properties.

Reviewer: P.Degano