Petri Nets

This is an invited tutorial-review paper on Petri nets-a graphical and mathematical modeling tool. Petri nets are a promising tool for describing and studying information processing systems that are characterized as being concurrent, asynchronous, distributed, parallel, nondeterministic, and/or stochastic. The paper starts with a brief review of the history and the application areas considered in the literature. It 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 graphsthe concurrent system model most amenable to analysis. In addition, the paper presents introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets.

[1]  Kensuke Hasegawa,et al.  A Synthesis Method for Petri Net with Prescribed Firing Sequence , 1985 .

[2]  P. Merlin,et al.  A Methodology for the Design and Implementation of Communication Protocols , 1976, IEEE Trans. Commun..

[3]  Joël Favrel,et al.  Generalized Petri Net Reduction Method , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  T. Murata.  State equation, controllability, and maximal matchings of petri nets , 1977 .

[5]  Eike Best,et al.  A Step Towards a Solution of the Liveness Problem in Petri Nets , 1977 .

[6]  T. Agerwala,et al.  Putting Petri nets to work , 1989 .

[7]  Peter Radford,et al.  Petri Net Theory and the Modeling of Systems , 1982 .

[8]  Tam-Anh Chu,et al.  A Method of Abstraction for Petri Nets , 1987, PNPM.

[9]  Michel Hack,et al.  The Recursive Equivalence of the Reachability Problem and the Liveness Problem for Petri Nets and Vector Addition Systems , 1974, SWAT.

[10]  Bernd J. Krämer,et al.  Stepwise construction of non-sequential software systems using a net-based specification language , 1984, European Workshop on Applications and Theory in Petri Nets.

[11]  Wolfgang Reisig,et al.  Petri Nets with Individual Tokens , 1982, Theor. Comput. Sci..

[12]  Lucia Pomello,et al.  Some equivalence notions for concurrent systems. An overview , 1985, Applications and Theory in Petri Nets.

[13]  Tadao Murata,et al.  Circuit theoretic analysis and synthesis of marked graphs , 1977 .

[14]  Alexandre Zenie,et al.  Colored Stochastic Petri Nets , 1985, PNPM.

[15]  Gérard Roucairol,et al.  Linear Algebra in Net Theory , 1979, Advanced Course: Net Theory and Applications.

[16]  Kishor S. Trivedi,et al.  Extended Stochastic Petri Nets: Applications and Analysis , 1984, Performance.

[17]  Edward L. Robertson,et al.  Properties of Conflict-Free and Persistent Petri Nets , 1978, JACM.

[18]  Y. Narahari,et al.  On the invariants of coloured Petri nets , 1985, Applications and Theory in Petri Nets.

[19]  Marco Ajmone Marsan,et al.  Performance models of multiprocessor systems , 1987, MIT Press series in computer systems.

[20]  P. C. Cross,et al.  Elementary matrix algebra , 1959 .

[21]  P. Ladet,et al.  Modelling and validation of complex systems by coloured Petri nets; Application to a flexible manufacturing system , 1985, European Workshop on Applications and Theory in Petri Nets.

[22]  Manuel Silva,et al.  A Package for Computer Design of Concurrent Logic Control Systems , 1982 .

[23]  William H. Sanders,et al.  Stochastic Activity Networks: Structure, Behavior, and Application , 1985, PNPM.

[24]  Gérard Berthelot,et al.  Petri Nets Theory for the Correctness of Protocols , 1982, PSTV.

[25]  Michael K. Molloy.  Discrete Time Stochastic Petri Nets , 1985, IEEE Transactions on Software Engineering.

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

[27]  Jean-Loup Baer,et al.  Model, Design, and Evaluation of a Compiler for a Parallel Processing Environment , 1977, IEEE Transactions on Software Engineering.

[28]  Grzegorz Rozenberg,et al.  Advances in Petri Nets 1985 , 1985, Lecture Notes in Computer Science.

[29]  Manuel Silva Suárez,et al.  On the Computation of Structural Synchronic Invariants in P/T Nets , 1988, European Workshop on Applications and Theory of Petri Nets.

[30]  Gregor von Bochmann,et al.  A Unified Method for the Specification and Verification of Protocols , 1977, IFIP Congress.

[31]  Robert M. Keller,et al.  Formal verification of parallel programs , 1976, CACM.

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

[33]  Tadao Murata,et al.  A Predicate-Transition Net Model for Parallel Interpretation of Logic Programs , 1988, IEEE Trans. Software Eng..

[34]  G. S. Hura,et al.  Program verification for microprocessors through Petri net modeling , 1985 .

[35]  Kunihiko Hiraishi,et al.  Analysis and control of discrete event systems represented by petri nets , 1988 .

[36]  Grzegorz Rozenberg.  Advances in Petri Nets 1987 , 1986, Lecture Notes in Computer Science.

[37]  Rüdiger Valk.  Self-Modifying Nets, a Natural Extension of Petri Nets , 1978, ICALP.

[38]  Guy Juanole,et al.  Specification and verification of distributed systems using prolog interpreted petri nets. , 1984, ICSE '84.

[39]  Alan Mycroft,et al.  On the Relationship of CCS and Petri Nets , 1984, ICALP.

[40]  Richard L. Tenney,et al.  The decidability of the reachability problem for vector addition systems (Preliminary Version) , 1977, STOC '77.

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

[42]  Ursula Goltz,et al.  Synchronic structure - a tutorial , 1985, Applications and Theory in Petri Nets.

[43]  Cristian Radu Zervos,et al.  Colored Petri Nets: Their Properties and Applications. , 1977 .

[44]  Michael K. Molloy.  Performance Analysis Using Stochastic Petri Nets , 1982, IEEE Transactions on Computers.

[45]  C. Ramchandani,et al.  Analysis of asynchronous concurrent systems by timed petri nets , 1974 .

[46]  Hartmann J. Genrich,et al.  The Calculus of Facts , 1976, MFCS.

[47]  J. Robert Jump.  Asynchronous Control Arrays , 1974, IEEE Transactions on Computers.

[48]  Michael K. Molloy.  A CAD Tool for Stochastic Petri-Nets , 1986, FJCC.

[49]  Kurt Lautenbach,et al.  The Analysis of Distributed Systems by Means of Predicate ? Transition-Nets , 1979, Semantics of Concurrent Computation.

[50]  Mary K. Vernon,et al.  Exact Performance Estimates for Multiprocessor Memory and Bus Interference , 1987, IEEE Transactions on Computers.

[51]  Stephen S. Yau,et al.  Software Design Representation Using Abstract Process Networks , 1980, IEEE Transactions on Software Engineering.

[52]  T. Murata.  Method for realizing the synchronic distance matrix of a marked graph , 1982 .

[53]  Willem R. van Biljon.  Extending Petri Nets for Specifying Man-Machine Dialogues , 1988, Int. J. Man Mach. Stud..

[54]  Hany H. Ammar,et al.  Analysis of the Generalized Stochastic Petri Nets by State Aggregation , 1985, PNPM.

[55]  S. Vajda,et al.  Integer Programming and Network Flows , 1970 .

[56]  Rüdiger Valk,et al.  Generalizations of Petri Nets , 1981, MFCS.

[57]  Kurt Jensen.  Coloured Petri Nets , 1992, EATCS Monographs in Theoretical Computer Science.

[58]  P. S. Thiagarajan,et al.  On the Interconnection of Asynchronous Control Structures , 1975, JACM.

[59]  Robert M. Keller,et al.  Parallel Program Schemata and Maximal Parallelism I. Fundamental Results , 1973, JACM.

[60]  Stéphane Natkin,et al.  Evaluation Based upon Stochastic Petri Nets of the Maximum Throughput of a Full Duplex Protocol , 1981, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets.

[61]  Y. Narahari,et al.  Coloured Petri net models for automated manufacturing systems , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[62]  Hany H. Ammar,et al.  Hierarchical models for systems reliability, maintainability, and availability , 1987 .

[63]  C. V. Ramamoorthy,et al.  Performance Evaluation of Asynchronous Concurrent Systems Using Petri Nets , 1980, IEEE Transactions on Software Engineering.

[64]  C. A. Petri,et al.  Concurrency Theory , 1986, Advances in Petri Nets.

[65]  Krishnaiyan Thulasiraman,et al.  Structure of the submarking-reachability problem and network programming , 1988 .

[66]  Michael D. Zisman,et al.  Representation, specification and automation of office procedures , 1977 .

[67]  Clarence A. Ellis,et al.  Office Information Systems and Computer Science , 1980, CSUR.

[68]  Roy H. Campbell,et al.  Formal semantics of a class of high-level primitives for coordinating concurrent processes , 2004, Acta Informatica.

[69]  Dan C. Marinescu,et al.  Stochastic High-Level Petri Nets and Applications , 1988, IEEE Trans. Computers.

[70]  Y. Edmund Lien,et al.  A note on transition systems , 1976, Information Sciences.

[71]  Michel Hack,et al.  Decidability Questions for Petri Nets , 1975, Outstanding Dissertations in the Computer Sciences.

[72]  Rüdiger Valk,et al.  Infinite Behaviour and Fairness , 1986 .

[73]  C. A. Petri.  "Forgotten Topics" of Net Theory , 1986, Advances in Petri Nets.

[74]  Alain Finkel,et al.  An Introduction to Fifo Nets-Monogeneous Nets: A Subclass of Fifo Nets , 1985, Theor. Comput. Sci..

[75]  Sol M. Shatz,et al.  STATIC ANALYSIS OF ADA PROGRAMS USING THE PETRI NET MODEL. , 1985 .

[76]  Tadao Murata,et al.  Proof Procedure and Answer Extraction in Petri Net Model of Logic Programs , 1989, IEEE Trans. Software Eng..

[77]  Kurt Lautenbach,et al.  Use of Petri Nets for Proving Correctness of Concurrent Process Systems , 1974, IFIP Congress.

[78]  T. Agerwala,et al.  Complete model for representing the coordination of asynchronous processes , 1974 .

[79]  Stephen D. Shapiro,et al.  A stochastic petri net with applications to modelling occupancy times for concurrent task systems , 1979, Networks.

[80]  Kurt Lautenbach,et al.  Synchronisationsgraphen , 2004, Acta Informatica.

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

[82]  Klaus Voss.  A net model of a local area network protocol , 1984, European Workshop on Applications and Theory in Petri Nets.

[83]  Mary K. Vernon,et al.  The GTPN Analyzer: Numerical Methods and User Interface , 1986, FJCC.

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

[85]  D. P. Mital,et al.  Fault diagnosis of alignment networks using Petri nets , 1984 .

[86]  Giorgio De Michelis,et al.  Superposed Automata Nets , 1980, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets.

[87]  Dino Mandrioli.  A Note on Petri Net Languages , 1977, Inf. Control..

[88]  G. Chiola,et al.  An accurate performance model of CSMA/CD bus LAN , 1986, European Workshop on Applications and Theory of Petri Nets.

[89]  Tadao Murata,et al.  Structure matrices for petri nets and their applications , 1985 .

[90]  H.-P. Lipp.  The Application of a Fuzzy Petri Net for Controlling Complex Industrial Processes , 1983 .

[91]  Tadao Murata,et al.  B-Fairness and Structural B-Fairness in Petri Net Models of Concurrent Systems , 1992, J. Comput. Syst. Sci..

[92]  Rüdiger Valk,et al.  Infinite behaviour and fairness in Petri nets , 1985, European Workshop on Applications and Theory in Petri Nets.

[93]  Raymond E. Miller,et al.  Homomorphisms between Models of Parallel Computation , 1982, J. Comput. Syst. Sci..

[94]  Kumkum Garg.  An Approach to Performance Specification of Communication Protocols Using Timed Petri Nets , 1985, IEEE Transactions on Software Engineering.

[95]  Jan Magott,et al.  Performance Evaluation of Concurrent Systems Using Petri Nets , 1984, Inf. Process. Lett..

[96]  Y. Edmund Lien.  Termination Properties of Generalized Petri Nets , 1976, SIAM J. Comput..

[97]  Wolfgang Reisig,et al.  Petri Nets: Applications and Relationships to Other Models of Concurrency , 1986, Lecture Notes in Computer Science.

[98]  Giorgio De Michelis,et al.  GAMERU: A language for the analysis and design of human communication pragmatics within organizational systems , 1986, European Workshop on Applications and Theory of Petri Nets.

[99]  Nicolae Stoica,et al.  Neuronal networks modelled by petri type nets with controllers , 1986 .

[100]  Jan van Leeuwen.  A partial solution to the reachability-problem for vector-addition systems , 1974, STOC '74.

[101]  James L. Peterson,et al.  Petri Nets , 1977, CSUR.

[102]  Hartmann J. Genrich,et al.  Predicate/Transition Nets , 1986, Advances in Petri Nets.

[103]  James L. Peterson,et al.  A Note on Colored Petri Nets , 1980, Inf. Process. Lett..

[104]  Peter Huber,et al.  Towards reachability trees for high-level Petri nets , 1985, European Workshop on Applications and Theory in Petri Nets.

[105]  Jerre D. Noe,et al.  A Petri Net model of the CDC 6400 , 1971, SIGOPS Workshop on System Performance Evaluation.

[106]  Toshimitsu Ushio,et al.  State feedback and modular control synthesis in controlled Petri nets , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[107]  C. A. Petri.  Modelling as a Communication Discipline , 1977, Performance.

[108]  Tadao Kasami,et al.  Decidable Problems on the Strong Connectivity of Petri Net Reachability Sets , 1977, Theor. Comput. Sci..

[109]  Stephen S. Yau,et al.  Distributed Software System Design Representation Using Modified Petri Nets , 1983, IEEE Transactions on Software Engineering.

[110]  Y. S. Kwong,et al.  On Reduction of Asynchronous Systems , 1977, Theor. Comput. Sci..

[111]  D. Munson.  Circuits and systems , 1982, Proceedings of the IEEE.

[112]  Eike Best.  COSY: Its Relation to Nets and CSP , 1986, Advances in Petri Nets.

[113]  Manuel Silva,et al.  A Simple and Fast Algorithm to Obtain All Invariants of a Generalized Petri Net , 1980, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets.

[114]  Anastasia Pagnoni.  A Fair Competition Between Two or More Partners , 1981, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets.

[115]  Carl G. Looney,et al.  Fuzzy Petri nets for rule-based decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[116]  A.A. Khan,et al.  On the determination of the solution of a class of Murata's state equation of Petri nets , 1981, Proceedings of the IEEE.

[117]  Giovanni Chiola,et al.  A Software Package for the Analysis of Generalized Stochastic Petri Net Models , 1985, PNPM.

[118]  Gianfranco Ciardo,et al.  Stochastic Petri Net Analysis of a Replicated File System , 1989, IEEE Trans. Software Eng..

[119]  Tadao Murata,et al.  Detection of Ada Static Deadlocks Using Petri Net Invariants , 1989, IEEE Trans. Software Eng..

[120]  Suhas S. Patil,et al.  COORDINATION OF ASYNCHRONOUS EVENTS , 1970 .

[121]  Joseph Sifakis,et al.  Fairness and related properties in transition systems — a temporal logic to deal with fairness , 1983, Acta Informatica.

[122]  Tadao Murata,et al.  Petri Nets and Marked Graphs–Mathematical Models of Concurrent Computation , 1982 .

[123]  Joseph Sifakis,et al.  Use of Petri nets for performance evaluation , 1977, Acta Cybern..

[124]  Wolfgang Reisig,et al.  Petri Nets: Central Models and Their Properties , 1986, Lecture Notes in Computer Science.

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

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

[127]  Joseph Sifakis,et al.  A Unified Approach for Studying the Properties of Transition Systems , 1982, Theor. Comput. Sci..

[128]  Robert A. Nelson,et al.  Casting Petri Nets into Programs , 1983, IEEE Transactions on Software Engineering.

[129]  Kurt Jensen.  How to Find Invariants for Coloured Petri Nets , 1981, MFCS.

[130]  T Murata,et al.  Reduction and expansion of live and safe marked graphs. , 1979 .

[131]  F. J. W. Symons.  Development and application of Petri net based techniques in Australia , 1987 .

[132]  Michel Diaz,et al.  Petri net based models for the specification and validation of protocols , 1984, European Workshop on Applications and Theory in Petri Nets.

[133]  Jonathan Billington,et al.  Protocol analysis using numerical Petri nets , 1985, Applications and Theory in Petri Nets.

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

[135]  Michel Hack,et al.  The Equality Problem for Vector Addition Systems is Undecidable , 1976, Theor. Comput. Sci..

[136]  Tadao Murata,et al.  Additional methods for reduction and expansion of marked graphs , 1981 .

[137]  Tadao Kasami,et al.  Three measures for synchronic dependence in Petri nets , 1983, Acta Informatica.

[138]  C. A. Petri.  Introduction to General Net Theory , 1979, Advanced Course: Net Theory and Applications.

[139]  Gérard Berthelot,et al.  Checking properties of nets using transformation , 1985, Applications and Theory in Petri Nets.

[140]  Bernard Berthomieu,et al.  The Design and Validation by Petri Nets of a Mechanism for the Invocation of Remote Servers , 1980, IFIP Congress.

[141]  Ajoy Kumar Datta,et al.  Synthesis of a Class of Deadlock-Free Petri Nets , 1984, JACM.

[142]  Jonathan Billington,et al.  PROTEAN: A High-Level Petri Net Tool for the Specification and Verification of Communication Protocols , 1988, IEEE Trans. Software Eng..

[143]  Jan Grabowski,et al.  The Decidability of Persistence for Vector Addition Systems , 1980, Information Processing Letters.

[144]  Tadao Murata,et al.  Stochastic Net Model for Self-Stability Measures of Fault Tolerant Clock Synchronization , 1987, PNPM.

[145]  Mary K. Vernon,et al.  SARA (System ARchitects Apprentice): Modeling, analysis, and simulation support for design of concurrent systems , 1986, IEEE Transactions on Software Engineering.

[146]  Kishor S. Trivedi,et al.  The Design of a Unified Package for the Solution of Stochastic Petri Net Models , 1985, PNPM.

[147]  E. Le Mer.  OVIDE: A SOFTWARE PACKAGE FOR VERIFYING AND VALIDATING PETRI NETS , 1983 .

[148]  P. Merlin,et al.  Recoverability of Communication Protocols - Implications of a Theoretical Study , 1976, IEEE Transactions on Communications.

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

[150]  S. Rao Kosaraju,et al.  Decidability of reachability in vector addition systems (Preliminary Version) , 1982, STOC '82.

[151]  P. Ladet,et al.  Generalized Inverses and the Calculation of Symbolic Invariants for Coloured Petri Nets , 1991 .

[152]  L. A. Cherkasova,et al.  From nets to logic and back in the specification of processes , 1987 .

[153]  Manuel Silva,et al.  PROGRAMMABLE LOGIC CONTROLLERS AND PETRI NETS: A COMPARATIVE STUDY , 1983 .

[154]  Jean-Loup Baer,et al.  A Survey of Some Theoretical Aspects of Multiprocessing , 1973, CSUR.

[155]  Jacques Vautherin.  Non-linear invariants for coloured Petri nets with interdependent tokens; application to the proof of parallel programs , 1985, Applications and Theory in Petri Nets.

[156]  Wil M. P. van der Aalst,et al.  Applications and Theory of Petri Nets , 1983, Informatik-Fachberichte.

[157]  Charles F. Walker.  ADDITIONAL BIBLIOGRAPHY , 1974, The Frank C. Brown Collection of NC Folklore.

[158]  Anatol W. Holt.  Coordination technology and Petri nets , 1985, Applications and Theory in Petri Nets.

[159]  Tadao Murata,et al.  Relevance of network theory to models of distributed/parallel processing☆ , 1980 .

[160]  Mary K. Vernon,et al.  A Generalized Timed Petri Net Model for Performance Analysis , 1985, IEEE Transactions on Software Engineering.

[161]  Masahiro Sowa,et al.  A Timed Petri Net Model and Simulation of a Dataflow Computer , 1985, PNPM.

[162]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[163]  Kurt Jensen,et al.  Petri Net Tool Overview 1986 , 1986, Advances in Petri Nets.

[164]  Manuel Silva.  Towards a synchrony theory for P/T nets , 1987 .

[165]  Francesco Tisato,et al.  Modeling the Ada Task System by Petri Nets , 1985, Comput. Lang..

[166]  Werner E. Kluge,et al.  Reduction, Data Flow and Control Flow Models of Computation , 1986, Advances in Petri Nets.

[167]  David Misunas,et al.  Petri nets and speed independent design , 1973, Commun. ACM.

[168]  Nancy G. Leveson,et al.  Safety Analysis Using Petri Nets , 1987, IEEE Transactions on Software Engineering.

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

[170]  E. Gressier,et al.  A Stochastic Petri Net Model for Ethernet , 1985, PNPM.

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

[172]  Michael Yoeli,et al.  Towards a Hierarchy of Nets , 1984, J. Comput. Syst. Sci..

[173]  Ernst W. Mayr.  An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..

[174]  Tadao Murata.  Synthesis of Decision-Free Concurrent Systems for Prescribed Resources and Performance , 1980, IEEE Transactions on Software Engineering.

[175]  Wilfried Brauer,et al.  Net Theory and Applications , 1980, Lecture Notes in Computer Science.

[176]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

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

[178]  Giorgio Bruno,et al.  Process-translatable Petri nets for the rapid prototyping of process control systems , 1986, IEEE Transactions on Software Engineering.

[179]  Sun-Yuan Kung,et al.  Timing Analysis and Design Optimization of VLSI Data Flow Arrays , 1986, ICPP.

[180]  Alexander H. Levis,et al.  Petri net representation of decision models , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[181]  C. A. Petri.  Fundamentals of a Theory of Asynchronous Information Flow , 1962, IFIP Congress.

[182]  Jack B. Dennis.  Modular, asynchronous control structures for a high performance processor , 1970 .

[183]  Hideki Yamasaki.  Normal Petri Nets , 1984, Theor. Comput. Sci..

[184]  Nobuo Saito,et al.  Predicate/Transition Net Simulation based on Concurrent Prolog(Software Science and Engineering) , 1985 .

[185]  Serge Haddad,et al.  Specification and properties of a cache coherence protocol model , 1986, European Workshop on Applications and Theory of Petri Nets.

[186]  Tadao Murata,et al.  Fair relation and modified synchronic distances in a petri net , 1985 .

[187]  Gerald Estrin,et al.  Modeling and Verification of Communication Protocols in Sara: The X.21 Interface , 1980, IEEE Transactions on Computers.

[188]  Robert Valette,et al.  Analysis of Petri Nets by Stepwise Refinements , 1979, J. Comput. Syst. Sci..

[189]  Fritz Krückeberg,et al.  Mathematical methods for calculating invariants in Petri nets , 1986, European Workshop on Applications and Theory of Petri Nets.

[190]  P. S. Thiagarajan,et al.  Some classes of live and safe Petri nets , 1987 .

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

[192]  Kurt Lautenbach,et al.  The Orderly Resolution of Memory Access Conflicts Among Competing Channel Processes , 1982, IEEE Transactions on Computers.

[193]  Michel Diaz,et al.  Modeling and Analysis of Communication and Cooperation Protocols Using Petri Net Based Models , 1982, Comput. Networks.

[194]  Grzegorz Rozenberg,et al.  Applications and theory of Petri nets : selected papers from the 3rd European Workshop on Applications and Theory of Petri Nets, Varenna, Italy, September 27-30, 1982 , 1983 .

[195]  Stefano Crespi-Reghizzi.  Petri Nets and Szilard Languages , 1977, Inf. Control..

[196]  Robert M. Keller.  Parallel Program Schemata and Maximal Parallelism II: Construction of Closures , 1973, JACM.

[197]  Manuel Silva,et al.  A Language for the Description of Concurrent Systems Modeled by Colored Petri Nets: Application to the Control of Flexible Manufacturing Systems , 1985 .

[198]  Sergio Cesare Brofferio.  A Petri Net Control Unit for High-Speed Modular Signal Processors , 1987, IEEE Trans. Commun..

[199]  Gérard Roucairol,et al.  FIFO-Nets , 1986, Advances in Petri Nets.

[200]  Glynn Winskel,et al.  Petri nets, morphisms and compositionality , 1985, Applications and Theory in Petri Nets.

[201]  Joseph Sifakis,et al.  Structural Properties of Petri Nets , 1978, MFCS.

[202]  Tadao Murata,et al.  Inconsistency check of a set of clauses using petri net reductions , 1988 .

[203]  Gary J. Nutt,et al.  Macro E-Nets for Representation of Parallel Systems , 1973, IEEE Transactions on Computers.

[204]  Eike Best,et al.  Systems of Open Paths in Petri Nets , 1975, International Symposium on Mathematical Foundations of Computer Science.