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

Two models for gene assembly in ciliates have been proposed and investigated in the last few years. The DNA manipulations postulated in the two models are very different: one model is intramolecular – a single DNA molecule is involved here, folding on itself according to various patterns, while the other is intermolecular – two DNA molecules may be involved here, hybridizing with each other. Consequently, the assembly strategies predicted by the two models are completely different. Interestingly however, the final result of the assembly (including the assembled gene) is always the same. We compare in this paper the two models for gene assembly, formalizing both in terms of pointer reductions. We also discuss invariants and universality results for both models.

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Two Models for Gene Assembly in Ciliates

Computation graphs for actor grammars

reduction graphs be ARG. It turns out that there are graphs in ARG that are not (isomorphic to) reduction graphs. To obtain a characterization we need one more property of reduction graphs: the ability to linearly order the vertices to resemble its (in general not unique) underlying legal string, as done in Fig. 11. To make this linear order of vertices explicit, we introduce a third set of edges, called merge edges , to the reduction graph as done in Fig. 14. s 2 2 7 7 4 4 7 7 3 3 5 5 3 3 4 4 2 2 6 6 5 5 6 6 t Fig. 14. Merge edges are added to the reduction graph of Fig. 11. Now, when is a set of edges M for G ∈ ARG a set of merge edges? Like desire edges, they have the properties that (1) the edges connect vertices with a common label and (2) each vertex except s and t is connected to exactly one merge edge. Moreover, M and the set E2 are disjoint – no desire edge is parallel to a merge edge. Finally, the reality edges and merge edges must allow for a path from s to t passing each vertex once. This last requirement is equivalent to the fact that the reality and merge edges induce a connected graph. If it is possible to add a set of merge edges to the graph, then it is not difficult to see that the graph is isomorphic to a reduction graph Ru. Indeed, we can identify such a u for this reduction graph by simply considering the alternating path from s to t over the reality and merge edges. The orientation (positiveness or negativeness) of each pointer is determined by the crossing or non crossing of the desire edges (exactly as we defined the notion of reduction graph). To characterize reduction graphs we need the notion of a pointer-component graph. Given an abstract reduction graph, a pointer-component graph describes how the labels of that abstract reduction graph are distributed among its connected components. Definition 5.14. Let G ∈ ARG. The pointer-component graph of G, denoted by PCG, is a multigraph (ζ, E, e), where ζ is the set of connected components of G, E = dom(G) and e is, for e ∈ E, defined by e(e) = {C ∈ ζ | C contains vertices labelled by e}. The pointer-component graph of G = Ru of Fig. 12 is given in Fig. 15. We have ζ = {C1, C2, C3, R} where R is the linear component and the other elements are cyclic components of Ru. It is shown in [7] that, surprisingly, G ∈ ARG has a set of merge edges precisely when the pointer-component graph PCG is a connected graph. In other words: Theorem 5.15 ([7]). An abstract reduction graph G is isomorphic to a reduction graph iff PCG is a connected graph. Computational nature of gene assembly in ciliates 21

Computational Nature of Gene Assembly in Ciliates

Reaction systems are a formal model for processes inspired by the functioning of the living cell. The underlying idea of this model is that the functioning of the living cell is determined by the interactions of biochemical reactions, and these interactions are based on the mechanisms of facilitation and inhibition. In this paper we first review the main notions of the basic model of reaction systems which is a qualitative model. Then we discuss various ways of taking into account quantitative properties. About the authors Andrzej Ehrenfeucht is a Professor in the Department of Computer Science, University of Colorado, Boulder, USA. Jetty Kleijn is a visiting fellow within the School of Computing Science, Newcastle University. Maciej Koutny obtained his MSc (1982) and PhD (1984) from the Warsaw University of Technology. In 1985 he joined the then Computing Laboratory of the University of Newcastle upon Tyne to work as a Research Associate. In 1986 he became a Lecturer in Computing Science at Newcastle, and in 1994 was promoted to an established Readership at Newcastle. In 2000 he became a Professor of Computing Science. Grzegorz Rozenberg is a Professor of Computer Science at Leiden University, The Netherlands, and an Adjunct Professor at the Department of Computer Science of University of Colorado at Boulder, U.S.A. He is the head of the Theoretical Computer Science group at Leiden Institute of Advanced Computer Science (LIACS), and the scientific director of Leiden Center for Natural Computing (LCNC). He has published more than 500 papers, 6 books, and is a (co-)editor of about 90 books. He is a member of an editorial board of about 20 journals and book series. He has been a member of the program committees and invited speaker for practically all major conferences in theoretical computer science in Europe. He is a Foreign Member of the Finnish Academy of Sciences and Letters, a member of Academia Europaea, and he is holder of Honorary Doctorates of the University of Turku, Finland, the Technical University of Berlin, Germany, and the University of Bologna, Italy. He has received the Distinguished Achievements Award of the European Association for Theoretical Computer Science "in recognition of his outstanding scientific contributions to theoretical computer science". He is a Highly Cited Researcher by ISI. Suggested keywords REACTION SYSTEM GENERALISED REACTION SYSTEM LIVING CELL NATURAL COMPUTING GENETIC REGULATORY NETWORK TRANSITION SYSTEM, MEASUREMENT FUNCTION APPROXIMATION SIMULATION Qualitative and Quantitative Aspe ts of a Model for Pro esses Inspired by the Fun tioning of the Living Cell Andrzej Ehrenfeu ht1, Jetty Kleijn2, Ma iej Koutny3, and Grzegorz Rozenberg1,2 1 Department of Computer S ien e, University of Colorado at Boulder 430 UCB Boulder, CO 80309-0430, U.S.A. andrzej s. olorado.edu 2 LIACS, Leiden University, 2300 RA, The Netherlands {kleijn,rozenber} lia s.nl 3 S hool of Computing S ien e, New astle University, NE1 7RU, UK ma iej.koutny n l.a .uk Abstra t. Rea tion systems are a formal model for pro esses inspired by the fun tioning of the living ell. The underlying idea of this model is that the fun tioning of the living ell is determined by the intera tions of bio hemi al rea tions, and these intera tions are based on the me hanisms of fa ilitation and inhibition. In this paper we rst review the main notions of the basi model of rea tion systems whi h is a qualitative model. Then we dis uss various ways of taking into a ount quantitative properties.

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Qualitative and Quantitative Aspects of a Model for Processes Inspired by the Functioning of the Living Cell

A text is a tripleτ=(λ,ρ1,ρ2) such that λ is a labeling function, andρ1 andρ2 are linear orders on the domain of λ; hence τ may be seen as a word (λ,ρ1) together with an additional linear orderρ2 on the domain of λ. The orderρ2 is used to give to the word (λ,ρ1) itsindividual hierarchical representation (syntactic structure) which may be a tree but it may be also more general than a tree. In this paper we introducecontext-free grammars for texts and investigate their basic properties. Since each text has its own individual structure, the role of such a grammar should be that of a definition of a pattern common to all individual texts. This leads to the notion of ashapely context-free text grammar also investigated in this paper.

Grzegorz Rozenberg

Papers

Two Models for Gene Assembly in Ciliates

Computation graphs for actor grammars

Computational Nature of Gene Assembly in Ciliates

Qualitative and Quantitative Aspects of a Model for Processes Inspired by the Functioning of the Living Cell

Context-free text grammars