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. >

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Petri nets: Properties, analysis and applications

Data Mining Practical Machine Learning Tools and Techniques

https://cmi.ac.in/~madhavan/courses/verification-2011/alur-dill-tcs-94.pdf

A theory of timed automata

物件導向軟體之架構(Object-Oriented Software Construction)探討

The Temporal Logic of Reactive and Concurrent Systems: Specification

"d t The notion of a "deterministic machine" or a e erministic language" (as opposed to their nondeterministic Counterparts) is one of the oldest and most investigated in the theory of computation and in formal language theory. One can however observe that whereas the notion of a deterministic machine is usually the natural one (in every situation there is at most one possible "move" the machine can make), the notion of a deterministic language is often not natural at all. In fact a deterministic language is almost always defined as a language which can be recognized by a deterministic machine, although in many cases the languages themselves are being defined by grammars rather than by machines. The typical situation is of the following kind: first a class of languages £ is defined by a class of grammars ~, then one finds an "equivalent" class of machines~, and then by considering ~ the deterministie subelass~ D of the class~one obtains the deterministic subclass £D of the class £. What subclass of ~ generates £D is mostly not understood at all, or, in the best case, it is the "translation" of~ D into the subclass of~, which could neither be called natural nor give any insight into the nature of the deterministic restriction. The basic difficulty lies in the fact that the notion of a deterministic language is defined via recognizers whereas the languages themselves are often defined in terms of generative devices. In this paper we want to point out several classes of languages for which the notion of "generative determinism" (deterministic restriction defined in terms of grammars rather than recognizers) is not only a very natural one but it also lends itself to mathamatical treatment. The theory of L systems and languages originated with the work of

/pdf/generatively-deterministic-l-languages-subword-point-of-view-m2azc9ov3i.pdf

Generatively Deterministic L Languages. Subword Point of View

Formal models for gene assembly in ciliates have been developed, in particular the string pointer reduction system (SPRS) and the graph pointer reduction system (GPRS). The reduction graph is a valuable tool within the SPRS, revealing much information about how gene assembly is performed for a given gene. The GPRS is more abstract than the SPRS and not all information present in the SPRS is retained in the GPRS. As a consequence the reduction graph cannot be defined for the GPRS in general, but we show that it can be defined (in an equivalent manner as defined for the SPRS) if we restrict ourselves to so-called realistic overlap graphs. Fortunately, only these graphs correspond to genes occurring in nature. Defining the reduction graph within the GPRS allows one to carry over several results within the SPRS that rely on the reduction graph.

How Overlap Determines the Macronuclear Genes in Ciliates

The classes of languages accepted by (unrestricted) PAC machines and (unrestricted) PDA2machines are characterized. Several extentions of the PAC machine model are defined and in particular: (i) a method is presented that for each class of K-iteration grammars provides a class ofacceptors for the corresponding class of languages, and (ii) it is shown that a simple (and natural) extension of a PDA2model yields a class of acceptors forthe class of recursively enumerable languages.

On acceptors of iteration languages

Map L-systems for theoretical cell division patterns provide clues for division patterns in real organisms, which are very often difficult to observe in great detail. From the map L-systems the combinatory of the cell division patterns can be investigated, and wall and cell growth functions can be determined (De Boer and Lindenmayer, 1987). The scope of the patterns that can be generated by map L-systems of a particular size and the architecture of the generated structures (archetypes) have been investigated exhaustively (LUck and LUck, 1986).

Panel discussion: The use of graph grammars in applications

0S systems generalize context-free grammars without nontermmals it is shown that it is decidable whether or not two arbitrary 0S systems generate the same set of (derivation) sequences It is obtained as a corollary that it is decidable whether or not two arbitrary context-free grammars have the same sets of derivation sequences

Grzegorz Rozenberg

Papers

Generatively Deterministic L Languages. Subword Point of View

How Overlap Determines the Macronuclear Genes in Ciliates

On acceptors of iteration languages

Panel discussion: The use of graph grammars in applications

The Sequence Equivalence Problem is Decidable for 0S Systems