Petri nets: an introduction
Semirings, automata, languages
Semirings, automata, languages
The theory of semirings with applications in mathematics and theoretical computer science
The theory of semirings with applications in mathematics and theoretical computer science
The Book of Traces
Rational, Linear and Algebraic Process Languages and Iteration Lemmata
Fundamenta Informaticae
A Hierarchy of Languages with Catenation and Shuffle
Fundamenta Informaticae - Concurrency, Specification and Programming
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Using general iteration lemmata for languages defined by rational, linear, and algebraic systems of equations on ω-complete semirings, it can be shown that such iteration lemmata hold for certain classes of word and trace languages, and for process algebra classes related to them. The basic operation has to be associative with a neutral element, and is extended to sets of elements, such that the structure defined by it together with union and ∅ is an ω-complete semiring. With this property rational, linear and algebraic systems of equations can be defined, having a unique minimal solution as least fixed points. To guarantee iteration lemmata for the corresponding rational, linear and algebraic classes, a norm on the structure has to exist, fulfilling some monotonicity on union and extended operation on sets. This article is an extended version of the paper presented at the workshop CS&P'98 in Berlin, September 28-30, 1998. (This paper has been presented on the workshop CS&P'98 at Berlin.)