Rational, Linear and Algebraic Process Languages and Iteration Lemmata

Authors:
Ludwik Czaja;Manfred Kudlek
Affiliations:
(Correspd.) Warsaw University e-mail: lczaja@mimuw.edu.pl;(Correspd.) Hamburg University e-mail: kudlek@informatik.uni-hamburg.de
Venue:
Fundamenta Informaticae
Year:
2000

Citing 8
Cited 0

Petri nets: an introduction

Petri nets: an introduction
Semirings, automata, languages

Semirings, automata, languages
Nonsequential processes

Nonsequential processes
Context-free languages

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The theory of semirings with applications in mathematics and theoretical computer science

The theory of semirings with applications in mathematics and theoretical computer science
Process languages and nets

Theoretical Computer Science
Net-Definability of Process Languages

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Iteration Lemmata for Certain Classes of Word, Trace and Graph Languages

Fundamenta Informaticae

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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. When extended to sets, we get an ω-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.