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## Rational, Linear and Algebraic Process Languages and Iteration Lemmata.

Czaja, Ludwik;
Kudlek, Manfred
In:
Burkhard, H.-D.; Czaja, L.; Nguyen, H.-S.; Starke, P.: *Proceedings of the CSP'99 Workshop, Warsaw, 28-30 September 1999*, pages 36-46.
1999.

Abstract:
In this paper we define a certain class of process languages viewing
processes as bipartite graphs with an associative operation (sequential
composition) on them. They describe finite evolutions of Petri nets.
Extended to sets we get an omega-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.

Keywords:
formal languages, iteration lemmata, processes, Petri nets.

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