Petri Nets: Basic Notions, Structure, Behaviour

We give a sketch of the theory of Petri nets. The aspects that we concentrate on are the basic notions of the theory and the interplay between the structure and behaviour of distributed systems as modelled by Petri nets. The theory we present is confined to a restricted class of Petri nets called safe Petri nets which correspond essentially to systems that have finite state spaces.

[1]  Antoni W. Mazurkiewicz.  Semantics of concurrent systems: a modular fixed-point trace approach , 1984, European Workshop on Applications and Theory in Petri Nets.

[2]  C. A. Petri.  State-transition structures in physics and in computation , 1982 .

[3]  P. S. Thiagarajan,et al.  On the Equivalence of Asynchronous Control Structures , 1973, SIAM J. Comput..

[4]  A. Mazurkiewicz.  Concurrent Program Schemes and their Interpretations , 1977 .

[5]  Rüdiger Valk,et al.  Formal Properties of Place/Transition Nets , 1979, Advanced Course: Net Theory and Applications.

[6]  Kurt Lautenbach,et al.  Substitution Systems - A Family of System Models Based on Concurrency , 1980, MFCS.

[7]  Rüdiger Valk.  Infinite Behaviour of Petri Nets , 1983, Theor. Comput. Sci..

[8]  P. S. Thiagarajan,et al.  D-Continuous Causal Nets: A Model of Non-Sequential Processes , 1984, Theor. Comput. Sci..

[9]  Wolfgang Reisig,et al.  The Non-sequential Behavior of Petri Nets , 1983, Inf. Control..

[10]  Eike Best.  A theorem on the characteristics of nonsequential processes , 1980, Fundam. Informaticae.

[11]  P. S. Thiagarajan,et al.  A Fresh Look at Free Choice Nets , 1984, Inf. Control..

[12]  James L. Peterson.  Computation Sequence Sets , 1976, J. Comput. Syst. Sci..

[13]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains, Part I , 1981, Theor. Comput. Sci..

[14]  P. S. Thiagarajan,et al.  A Theory of Bipolar Synchronization Schemes , 1984, Theor. Comput. Sci..

[15]  Amir Pnueli,et al.  Marked Directed Graphs , 1971, J. Comput. Syst. Sci..

[16]  Richard M. Karp,et al.  Parallel Program Schemata , 1969, J. Comput. Syst. Sci..

[17]  Kurt Jensen,et al.  Coloured Petri Nets and the Invariant-Method , 1981, Theor. Comput. Sci..

[18]  Kurt Lautenbach,et al.  Elements of General Net Theory , 1979, Advanced Course: Net Theory and Applications.

[19]  Józef Winkowski,et al.  Behaviours of Concurrent Systems , 1980, Theor. Comput. Sci..

[20]  Glynn Winskel,et al.  Events in computation , 1980 .

[21]  Wolfgang Reisig.  Petri Nets: An Introduction , 1985, EATCS Monographs on Theoretical Computer Science.

[22]  Grzegorz Rozenberg,et al.  Subset Languages of Petri Nets Part I: The Relationship to String Languages and Normal Forms , 1983, Theor. Comput. Sci..

[23]  César Fernández.  Non-sequential Processes , 1986, Advances in Petri Nets.

[24]  Eike Best,et al.  The Relative Strength of K-Density , 1979, Advanced Course: Net Theory and Applications.

[25]  Peter H. Starke.  Free Petri Net Languages , 1978, MFCS.

[26]  Matthias Jantzen,et al.  On the hierarchy of Petri net languages , 1979, RAIRO Theor. Informatics Appl..

[27]  C. Petri.  Grundsätzliches zur Beschreibung Diskreter Prozesse , 1967 .

[28]  Michel Hack,et al.  ANALYSIS OF PRODUCTION SCHEMATA BY PETRI NETS , 1972 .

[29]  P. S. Thiagarajan,et al.  A note on observable occurrence nets , 1985, European Workshop on Applications and Theory in Petri Nets.

[30]  Eike Best,et al.  A Theorem on the Characteristics of Non-sequential Processes , 1977 .

[31]  Kurt Lautenbach,et al.  System Modelling with High-Level Petri Nets , 1981, Theor. Comput. Sci..