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w-Process Languages for Place/Transition Nets

Czaja L., Kudlek M.

Fundamenta Informaticae

2001

Vol. 47, nr 3,4

217-229

The definition of process admitted here follows the line developed for elementary (1-safe) Petri nets and published in [Cza 99], [Cza 2000a], [Cza-Kud 2000]. It pertains not to any particular net, thus allows for collecting processes into arbitrary sets, i.e. process languages, and for asking questions like: for a given process language decide if there exists a Place/Transition net and if yes, contruct it (synthesis). The collection of all process languages is a semantic domain for Place/Transition nets. w-process languages contain both finite and infinite processes. The main problems pursued are analysis, synthesis and iteration lemmata for w-process languages. Surprisingly, the problems enjoy much simpler solutions for processes generated by P/T nets than generated by elementary nets.

Rational, Linear and algebraic process languages and iteration lemmata

Czaja L., Kudlek M.

Fundamenta Informaticae

2000

Vol. 43, Nr 1-4

49-60

In this paper we define a certain class of process languages viewing processes as bi-partite graphs with an associative operation (sequential composition) on them. They describe finite evolutions of Petri nets. When extended to sets, we get an w-complete semiring such that rational, linear, and algebraic sets of such processes can be defined as least fixed points of systems of equations. With a norm of processes also iteration lemmata can be obtained. Finally, we also present a related structure of directed acyclic graphs.