On the Algebraic Structure of Petri Nets

This paper retraces, collects, and summarises the contributions of the author --- both individually and in collaboration with others --- on the theme of algebraic, compositional approaches to the semantics of Petri nets.

[1]  Grzegorz Rozenberg,et al.  Petri Nets: Basic Notions, Structure, Behaviour , 1986, Current Trends in Concurrency.

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

[3]  José Meseguer,et al.  From Petri Nets to Linear Logic through Categories: A Survey , 1991, Int. J. Found. Comput. Sci..

[4]  C. C. Elgot.  Monadic Computation And Iterative Algebraic Theories , 1982 .

[5]  Matthew Hennessy,et al.  Algebraic theory of processes , 1988, MIT Press series in the foundations of computing.

[6]  Paolo Baldan,et al.  Modelling Concurrent Computations: from Contextual Petri Nets to Graph Grammars , 2000 .

[7]  Raymond R. Devillers,et al.  Sequential and Concurrent Behaviour in Petri Net Theory , 1987, Theor. Comput. Sci..

[8]  Wolfgang Reisig,et al.  Place or Transition Petri Nets , 1996, Petri Nets.

[9]  Carolyn Brown,et al.  Temporal Logic and Categories of Petrie Nets , 1993, ICALP.

[10]  Nicoletta Sabadini,et al.  Bicategories of processes , 1997 .

[11]  Z. Ésik,et al.  Iteration Theories: The Equational Logic of Iterative Processes , 1993 .

[12]  Albert Koelmans,et al.  Petri Nets and Digital Hardware Design , 1998 .

[13]  Roberto Bruni,et al.  Functorial semantics for Petri nets under the individual token philosophy , 1999, CTCS.

[14]  Glynn Winskel,et al.  Event Structure Semantics for CCS and Related Languages , 1982, ICALP.

[15]  Vladimiro Sassone,et al.  An Axiomatization of the Algebra of Petri Net Concatenable Processes , 1996, Theor. Comput. Sci..

[16]  Gheorghe Stefănescu,et al.  On Flowchart Theories: Part II. The Nondeterministic Case , 1987, Theor. Comput. Sci..

[17]  Samson Abramsky,et al.  Retracing some paths in Process Algebra , 1996, CONCUR.

[18]  Grzegorz Rozenberg,et al.  Transition Systems, Event Structures and Unfoldings , 1991 .

[19]  Józef Winkowski.  An Algebraic Description of System Behaviours , 1982, Theor. Comput. Sci..

[20]  Michael Pfender,et al.  Universal algebra in s-monoidal categories , 1974 .

[21]  Søren Christensen,et al.  Coloured Petri Nets Extended with Place Capacities, Test Arcs and Inhibitor Arcs , 1992, Application and Theory of Petri Nets.

[22]  Gheorghe Stefanescu,et al.  On Flowchart Theories. I. The Deterministic Case , 1987, J. Comput. Syst. Sci..

[23]  Kurt Jensen,et al.  Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use. Vol. 1, Basic Concepts , 1992 .

[24]  José Meseguer,et al.  Representation Theorems for Petri Nets , 1997, Foundations of Computer Science: Potential - Theory - Cognition.

[25]  Ugo Montanari,et al.  On the semantics of place/transition Petri nets , 1997, Mathematical Structures in Computer Science.

[26]  Wolfgang Reisig,et al.  Lectures on Petri Nets I: Basic Models , 1996, Lecture Notes in Computer Science.

[27]  Glynn Winskel,et al.  Completeness Results for Linear Logic on Petri Nets , 1993, Ann. Pure Appl. Log..

[28]  Maciej Koutny,et al.  Petri Nets, Process Algebras and Concurrent Programming Languages , 1996, Petri Nets.

[29]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[30]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains , 1979, Semantics of Concurrent Computation.

[31]  Walter Vogler,et al.  Partial order semantics and read arcs , 1997, Theor. Comput. Sci..

[32]  Davide Sangiorgi,et al.  Communicating and Mobile Systems: the π-calculus, , 2000 .

[33]  Antoni W. Mazurkiewicz,et al.  Trace Theory , 1986, Advances in Petri Nets.

[34]  Einar Smith.  Principles of High-Level Net Theory , 1996, Petri Nets.

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

[36]  Glynn Winskel,et al.  Petri Nets, Algebras, Morphisms, and Compositionality , 1987, Inf. Comput..

[37]  Joost Engelfriet,et al.  Elementary Net Systems , 1996, Applications and Theory of Petri Nets.

[38]  Jörg Desel,et al.  Process Semantics of Petri Nets over Partial Algebra , 2000, ICATPN.

[39]  E. S. Bainbridge.  Feedback and Generalized Logic , 1976, Inf. Control..

[40]  Roberto Bruni,et al.  Algebraic Models for Contextual Nets , 2000, ICALP.

[41]  R. Street,et al.  Review of the elements of 2-categories , 1974 .

[42]  Glynn Winskel,et al.  Event Structures , 1986, Advances in Petri Nets.

[43]  Roberto Gorrieri,et al.  A Petri Net Semantics for pi-Calculus , 1995, CONCUR.

[44]  Roberto Bruni,et al.  Zero-Safe Nets: Comparing the Collective and Individual Token Approaches , 2000, Inf. Comput..

[45]  Madhavan Mukund.  Petri Nets and Step Transition Systems , 1992, Int. J. Found. Comput. Sci..

[46]  Fabio Gadducci,et al.  Axioms for Contextual Net Processes , 1998, ICALP.

[47]  Bernd Grahlmann,et al.  The State of PEP , 1999, AMAST.

[48]  S. Maclane,et al.  Categories for the Working Mathematician , 1971 .

[49]  Roberto Gorrieri,et al.  Implicative formulae in the proofs of computations' analogy , 1989, POPL '90.

[50]  Kurt Jensen,et al.  Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use. Vol. 3, Practical Use , 1997 .

[51]  Maciej Koutny,et al.  Semantics of Inhibitor Nets , 1995, Inf. Comput..

[52]  Masahito Hasegawa,et al.  Recursion from Cyclic Sharing: Traced Monoidal Categories and Models of Cyclic Lambda Calculi , 1997, TLCA.

[53]  Ernst-Rüdiger Olderog,et al.  Nets, terms and formulas , 1991 .

[54]  Grzegorz Rozenberg,et al.  Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency , 1988, Lecture Notes in Computer Science.

[55]  José Meseguer,et al.  Process versus Unfolding Semantics for Place/Transition Petri Nets , 1996, Theor. Comput. Sci..

[56]  Vladimiro Sassone,et al.  Petri Nets and Other Models of Concurrency , 1996, Petri Nets.

[57]  Rob J. van Glabbeek,et al.  Petri Net Models for Algebraic Theories of Concurrency , 1987, PARLE.

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

[59]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[60]  Vladimiro Sassone,et al.  Characterizing Behavioural Congruences for Petri Nets , 1995, CONCUR.

[61]  Robin Milner.  Action Calculi, or Syntactic Action Structures , 1993, MFCS.

[62]  C. A. Petri.  Concepts of Net Theory , 1973, MFCS.

[63]  Hartmut Ehrig,et al.  A Uniform Approach to Petri Nets , 1997, Foundations of Computer Science: Potential - Theory - Cognition.

[64]  José Meseguer,et al.  Petri Nets Are Monoids , 1990, Inf. Comput..

[65]  Roberto Bruni,et al.  Executing Transactions in Zero-Safe Nets , 2000, ICATPN.

[66]  Wolfgang Reisig,et al.  System Design Using Petri Nets , 1983, Requirements Engineering.

[67]  G. M. Kelly,et al.  On MacLane's conditions for coherence of natural associativities, commutativities, etc. , 1964 .

[68]  Roberto Bruni,et al.  Functorial Models for Petri Nets , 2001, Inf. Comput..

[69]  Julia Padberg,et al.  Abstract Petri Nets as a Uniform Approach to High/Level Petri Nets , 1998, WADT.

[70]  Valeria de Paiva,et al.  A Linear Specification Language for Petri Nets , 1991 .

[71]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

[72]  Vladimiro Sassone,et al.  An axiomatization of the category of Petri net computations , 1998, Mathematical Structures in Computer Science.

[73]  David B. Benson.  The Basic Algebraic Structures in Categories of Derivations , 1975, Inf. Control..

[74]  Wolfgang Reisig,et al.  Informal Introduction to Petri Nets , 1996, Applications and Theory of Petri Nets.

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

[76]  Glynn Winskel,et al.  Relational Semantics of Non-Deterministic Dataflow , 1997 .

[77]  Glynn Winskel,et al.  A New Definition of Morphism on Petri Nets , 1984, STACS.

[78]  Christos T. Karamanolis,et al.  Elements of distributed algorithms-modeling and analysis with petri nets Wolfgang Reisig [Book review] , 1999, IEE Proceedings - Software.

[79]  Wojciech Zielonka,et al.  The Book of Traces , 1995 .

[80]  P. S. Thiagarajan,et al.  A Trace Semantics for Petri Nets , 1995, Inf. Comput..

[81]  Wolfgang Reisig,et al.  Lectures on Petri Nets II: Applications , 1996, Lecture Notes in Computer Science.

[82]  Roberto Gorrieri,et al.  SCONE: A Simple Calculus of Nets , 1990, CONCUR.

[83]  G. Michele Pinna,et al.  Non Sequential Semantics for Contextual P/T Nets , 1996, Application and Theory of Petri Nets.

[84]  Ross Street,et al.  Traced monoidal categories , 1996 .

[85]  C. Petri.  Kommunikation mit Automaten , 1962 .

[86]  P. S. Thiagarajan,et al.  Local Event Structures and Petri Nets , 1993, CONCUR.

[87]  Saunders MacLane,et al.  Natural Associativity and Commutativity , 1963 .

[88]  Ugo Montanari,et al.  An Event Structure Semantics for P/T Contextual Nets: Asymmetric Event Structures , 1998, FoSSaCS.

[89]  Kurt Jensen,et al.  Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use. Vol. 2, Analysis Methods , 1992 .