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**Compositional semantics of pure place/transition systems.**
*(English)*
Zbl 0676.68030

Advances in Petri nets, APN, Proc. 8th Eur. Workshop, Zaragoza/Spain 1987, Lect. Notes Comput. Sci. 340, 307-330 (1988).

[For the entire collection see Zbl 0658.00014.]

Author’s summary: “Following the ideas included in A. Mazurkiewicz [Semantics of concurrent systems: A modular fixed-point trace approach, Lect. Notes Comput. Sci. 188, 353-375 (1985; Zbl 0576.68044)] we consider P/T nets as constituting a support of an algebra \(APT=(PT,+)\) where \(+\) is a binary operation of net composition. It turns out that APT has a class of free generators (atomic nets). As the behaviour of nets we take prefix closed qualified languages (sets of qualified pomsets). The class of such languages form another algebra \(AQL=(QL\), ), where is a binary operation of qualified languages synchronization; this operation consists in all possible pairwise synchronization of qualified pomsets belonging to arguments of the synchronization. The compositional semantics of P/T nets is a homomorphism from APT to AQL; since APT has atomic nets as its class of free generators, each mapping of atomic nets into qualified languages can be uniquely extended to a semantics of P/T nets. Since the key notion of the whole construction is that of synchrnization, the main part of the paper is devoted to this operation and its properties.”

Author’s summary: “Following the ideas included in A. Mazurkiewicz [Semantics of concurrent systems: A modular fixed-point trace approach, Lect. Notes Comput. Sci. 188, 353-375 (1985; Zbl 0576.68044)] we consider P/T nets as constituting a support of an algebra \(APT=(PT,+)\) where \(+\) is a binary operation of net composition. It turns out that APT has a class of free generators (atomic nets). As the behaviour of nets we take prefix closed qualified languages (sets of qualified pomsets). The class of such languages form another algebra \(AQL=(QL\), ), where is a binary operation of qualified languages synchronization; this operation consists in all possible pairwise synchronization of qualified pomsets belonging to arguments of the synchronization. The compositional semantics of P/T nets is a homomorphism from APT to AQL; since APT has atomic nets as its class of free generators, each mapping of atomic nets into qualified languages can be uniquely extended to a semantics of P/T nets. Since the key notion of the whole construction is that of synchrnization, the main part of the paper is devoted to this operation and its properties.”

Reviewer: F.-L.Tiplea