Grzegorz Rozenberg

Bio: Grzegorz Rozenberg is an academic researcher from Leiden University. The author has contributed to research in topics: Petri net & Formal language. The author has an hindex of 81, co-authored 679 publications receiving 31378 citations. Previous affiliations of Grzegorz Rozenberg include Åbo Akademi University & University of Warsaw.

Behaviour of Elementary Net Systems

Abstract: We consider two ways of recording the behaviour of an elementary net system (EN system): via sequential observations and via non-sequential observations. In the sequential point of view each record of the behaviour of an EN system is a string of event occurrences (called a firing sequence) as registered by a sequential observer. In the nonsequential point of view we can define the behaviour of an EN system by either extracting causal order of events from firing sequences (obtaining firing traces) or by recording all nonsequential observations of event occurrences and of resulting holdings of conditions (each such record is called a process). In our contribution we discuss each of the three approaches and then relate them to each other.

TOL systems and languages

Abstract: We discuss a family of systems and languages (called TOL) which have originally arisen from the study of mathematical models for the development of some biological organisms. From a formal language theory point of view, a TOL system is a rewriting system where at each step of a derivation every symbol in a string is rewritten in a context-free way, but different rewriting steps may use different sets of production rules and the language consists of all strings derivable from the single fixed string (the axiom). The family of TOL languages (as well as its different subfamilies considered here) is not closed with respect to usually considered operations; it is “incomparable” with context-free languages, but it is contained in the family of context-free programmed languages. TOL languages form an infinite hierarchy with respect to “natural” complexity measures introduced in this paper.

Petri nets: Properties, analysis and applications

Abstract: Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >