Petri NetsPN ReferencesPN AnthologiesER Models

Evolution of Petri Nets

Last update: 7 July 2005
Number of models: 115

This site contains a sample of Petri nets (PN). The short citation refers to the reference used for evaluation. There may be alternative publications, which have the same content. In the year stated, the Petri net was mentioned for the first time, according to the year of the conference, additional materials or information by the author. Consequently, it may differ from the year of the reference. Any special names of the new Petri nets are listed. If the ancestor of a new Petri net is explicitly stated in the reference, it can be found in the column descendant of. In the columns, the following abbreviations have been used: Some papers on theoretical and practical problems of Petri nets as well as PN analogies, PN homologies and PN surveys are contained in the list of references. The evolution of ER models has been investigated as well.

Show the following columns:
Short CitationYearSpecial NameDescendant ofConstructsSyntactic RulesRemarksCauseAlternative PublicationsBinary Vector (Inherent)Binary Vector (Explicit)Binary Vector (Domain-Specifics)Expressiveness ValuesPartially Redundant Constructs
No. Short Citation Year Special Name Descendant of Constructs Syntactic Rules RemarksCause Alternative Publications Binary Vectors Expressiveness ValuesPartially Redundant Constructs
InherentNew Added RestrictedCitation                                            ContentInherentExplicitDomain-Specifics Total Inherent Explicit Domain Specific Linked Concepts Conjunctive Concepts
Place Transition Flow Relation Token InventedBorrowed Description Analysis Applicability Integration Prompted by Domain Other[P1] [P2] [P3] [P4] [P5] [P6] [P7] [P8] [P9] [P10] [P11] [P12] [P13] [P14] [P15] [P16] [P17] [P18] [P19] [P20] [P21] [P22] [P23] [P24] [P25] [P26] [P27] [P28] [P29] [P30] [P31]
1(Petri 1962)1962A-NetzXX, (r: Aktion)Xr: Tobit(1) Each place is connected to at least one transition. (2) Tobits can be assigned to places.Die Arbeit befaßt sich mit den begrifflichen Grundlagen einer Theorie der Kommunikation. Die Aufgabe dieser Theorie soll es sein, möglichst viele Erscheinungen bei der Informationsübertragung und Informationswandlung in einheitlicher und exakter Weise zu beschreiben (S. 1). ... Die Theorie liefert ein Darstellungsmittel für komplizierte organisatorische Vorgänge beliebiger Art (S. 3).g
1+(Holt 1968)1968Petri-Net (C/E-Net: Condition/Event) XXr: input/putput relationsX(1) A flow connects either a place to a transition or vice versa. (2) Places can carry tokens.not counted, because no new information is added... aimed at developing theory and technique for the analysis and description of data structures (p. 1).g X[Petri 1973], [Petri 1977]
2(Genrich 1969)1969Synchronisationsgraphr: Kantenr: Knoten(X)r: MarkeXEach "Knoten" has exactly one input ("Eingang") and exactly one output ("Ausgang").Im folgenden soll gezeigt werden, dass und wie dieses Problem (Zollstationenproblem; the author) gelöst werden kann (p.1).X[Genrich/Lautenbach 1973]nanananananananananananananananananananananananananananananananananananana
3a(Holt/Commoner 1970)1970Marked GraphC/EXXXXXEach place has at most one input transition and at most one output transition.Marked graphs and state machine graphs are counted together.It became clear that a direct approach to the analysis of occurrence systems was too difficult and we backed of to the study of two simpler classes of structures: marked graphs and state transition diagrams (p. 4).X0.
3b(Holt/Commoner 1970)1970State Machine GraphC/EXXXXXEach transition has at most one input place and at most one output place.see above; not counted------nanananananananananananananananananananananananananananananananananananana
4(Patil 1970)1970Coordination NetC/EXsg: input, output, internalXr: stoneconstraint set(1) Each constraint set is defined on a set of places. Coordination nets for representing such coordination (abstract). Coordination nets do not add more variety to the class of coordinations represented by Petri nets, but they make representation simple and manageable (p. 28).X110.
5(Hack 1972)1972Free Choice NetP/TXXXXXEvery arc from a place to a transition is either the unique output arc of the place or the unique input arc to the transition.... it appears difficult to fully understand the relationships between the structure of the net ... and the behavior of the net ... . Hence we approach the problem by analyzing first certain restricted subclasses of Petri Nets (p. 13).Xnanananananananananananananananananananananananananananananananananananana
6(Nutt 1972a)1972E-Nets (Evaluation Net)C/Er: location, sg: peripheral, resolutionsg/l: type (T-,F-, J-, X-, Y-transition), sg/f: transition timeXsg: attribute tokenX(1) The maximum number of locations connected to a transition is limited to 4. (2) A location may have, at most, one edge directed in and one edge directed out.A class of models will be introduced in this paper that is specifically intended to make performance evaluation more attainable ....(p. 3). ... evaluation nets require that there be some time associated with each action of a transition (p. 24).timeXperformance evaluation(Nutt 1972b)111110.
7(Agerwala/Flynn 1973)1973P/Tsg: 'contrary'sg: OR-inputsg: inhibitorXA transition will place a token in a 'contrary' place P only if P = 0.... quite powerful, with respect to its capability for representing coordinations (p. 81).coodination1110.
8(Baer 1973a)1973rf: P/T, sg: switchrf: P/T, XOR-transitionrf: P/T, sg: absorberrf: P/TX(1) A transition that has a switch in its preset has exactly two places in its postset. ... to build models for parallel computation for some special class of algorithms ... (p. 13).dalgorithms(Baer 1973a)1110.
9(Noe/Nutt 1973)1973Macro E-NetsE-Netsrf: E-Nets, sg: macro location (Q)rf: E-Nets, sg: macro transition (X, Y, A, RH)rf: E-netsrf: E-netsXThe X-transition is analogous to a switch..... to provide means for more succinct visual display of the systems under consideration (p. 719). Representational convenience and clarity is greatly enhanced by the use of macro nets (p. 721).X11111110.230.400.170.00S
10(Ramachandi 1973)1973TPN (Timed Petri Nets)P/Trf: P/Tsg/f: firing timeXXXThis [existing Petri nets; the author] model ... does not contain information regarding the speed of operation of system components or any information about statistical utilization of the parts of a system. We show how such information can be incorporated into the model (pp. 9-10). ... motivated by the desire to study performance issues .... (p. 10).timeperformance evaluationm10.
11(Fuss 1975)1974P-T-Netze (Puffer/Transition)P/Tr: Puffer, sg: Steuer r: Transaktorenrf: P/Trf: P/TX... ergab sich aus dem Abwägen der praktischen Belange... (p. 326)X110.
12(Noe 1980a)1975Pro-NetE-Netssg/l: boundssg/l: procedure, firing delays (interval)sg: AND-logic, selectorrf: E-netglobal variables(1) Global variables are accessible to all procedures.Yet, when one wishes to express the complexities of actual computing systems, and deal with performance questions typically asked about them, one needs further capabilities that are attunded to the application ... (p. 347). ... many of the driving forces in this evolution of method have related to the problems of abstraction (p. 358).structureperformance evaluation1111110.190.330.170.00
13(Merlin/Farber 1976)1976TPN (Time Petri Net)C/EXsg/l: firing delay intervalXXX.... which permits the formal analysis and synthesis of recoverable computer communication protocols (p. 1036) ... the TPN which ... includes a way of representing limits in the execution time of its parts (p. 1037).time protocols10.
14(Symons 1980)1976NPN (Numerical Petri Net)P/Tsg/f: operationsg/l: enabling conditionsg/l: valuesmemoryTransitions can access memory.... overcome in a simple way the basic limitations of Petri nets to model some types of practical systems (p. 28). .. adding ... descriptive power (p. 29). ... overcome the inability of Petri nets to model the handling of numerical information in a packet switching protocol (p. 29).dprotocols11110.
15(Sifakis 1980)1977TPTN (Timed Place-Transition Nets)P/T (, TPN)rf: P/T, sg/f: time base rf: P/Trf: P/Trf: P/T, sg: available/unavailableXThe use of asynchronous models for performance evaluation necessitates that they be augmented by introducing a time parameter ... (p. 307).timeperformance evaluation1110.
16(Valette 1977)1977Control GraphP/Tsg: idlesg/l: logical function, operatorsXThe idle place has one and only one successor as well as one and only one predecessor transition.Petri nets .. have proved to be limited (p. 102). A model for the description and the analysis of a parallel control system has been given (p. 107).g X1110.
17(Genrich/Lautenbach 1978)1978P/T (Place/Transition)sg: capacitiesXsg/f: weightedXXunknown------
18(Moalla et al. 1978)1978SPN (Synchronized Petri Nets)P/Trf: P/Trf: P/Trf: P/Trf: P/Tevent(1) Events are assigned to transitions..... (SPN) which permit the description of synchronous non-autonomous systems (p. 375).sychronization, non-autonomym100.
19(Schiffers/Wedde 1978)1978CP-Nets (Coloured Petri-Nets)P/Trf: P/Trf: P/Trf: P/Tsg: colouredXEach source place is assigned exactly one target place through a transition (stream)... for describing the process structure ... (p. 463).structurei1i0.
20(Valk 1978a)1978Self-Modifying NetsP/Trf: P/Trf: P/Tsg/l: marked placesrf: P/TXWe now introduce an extension, called self-modifying nets, which includes the previous ones (p. 526). X(Valk 1978b)
21(Genrich/Lautenbach 1981)1979PrT (Predicate/Transition)C/E, P/Tsg: predicates, sg/f: capacitysg/l: logical formulas, sg: deadsg/l: formal sumssg: items (n-tupels of individual symbols)XOur model ... adds to the modelling power and complexity of Petri nets a new dimension, namely the formal treatment of individuals and their changing properties and relations (p. 110). individuals11m0.
22(Oberquelle 1980)1979CA-nets (Channel/Agency nets); MA-nets (Means/Activities)sd: channel, meanssd: agency, activitiessd: takes/puts, necessary/resultsd: message... new interpretations arising from teaching necessities (p. 483), ... representation (p. 481).dteaching10.
23(Shapiro 1979a)1979RPN (Random Petri Net)C/Erf: C/Erf: C/Esg: random switchrf: C/EX... having the possibility of branching the selection of successors to a task may take place at random ... (p. 375). ...arises from ... the design of fault tolerant systems (p. 375).uncertaintyfault tolerant systemsi0.
24(Shapiro 1979b)1979C/Esd: complex conditionsd: activity, violations, sg: factrf: C/Erf: C/EtransmissionA transmission passes through an activity and connects complex conditions.... facilitate the design and construction of information systems ... (p. 107)dsoftware1110.
25(Florin/Natkin 1982)1980SPN (Stochastic Petri Nets)P/Trf: P/Tsg/l: stochastically delayed (arbitrary distribution function)XXXunknown------
26(Hinderer 1982)1980A-nets (Algebraic nets)C/EXsd/l: polynomial semiringXXX... they [A-nets, the author] are designed to the purpose of categorical considerations (p. 142).dmathematics0.
27(Yoeli 1982)1980Extended Petri NetsP/Trf: P/Tsg/f: condition function, action functionXXX... is a powerful and convenient tool for the formal specification of .. cooperating sequential processes and communication protocols (p. 183).dprotocols110.
28(De Cindio et al. 1982)1981SA nets (Superposed Automata)PrTrf: PrTrf: PrTrf: PrTrf: PrTXnumber of incoming arc of a transition = number of outgoing arcs... to support system verification and evaluation (p. 269)X[De Cindio et al. 1987]nanananananananananananananananananananananananananananananananananananana
29(Molloy 1982)1981SPN (Stochastic Petri Nets)P/Trf: P/Tsg/l: transition rate (exponentially distributed firing time)XXX... [existing approaches, the author] have omitted any study of timing considerations. ... include timing as a specification (p. 914).time110.
30(Jensen 1981)1981CP81-Nets (Coloured Petri nets)PrTsg/f: colour setsg/f: colour setsg/l: functions denoting formal sumssg: colouredX What we do claim is that we have developed an alternative method for the analysis of these kinds of nets. .. it makes the method more transparent and we give an example where a proof in [1] is simplified considerably (p. 318).X(Jensen 1987a)
31(Coolahan/Roussopoulos 1983)1983TPN, P/Trf: P/T, sg/l: execution timesg: immediateXXX... an extension to the classic Petri net definition to incorporate the notion of time (p. 604).timem110.100.070.330.00
32(Jensen 1983)1983CPN (Coloured Petri nets)CP81-nets, PrTsg/f: colour setsg/f: colour set, sg/f: guardsg/l: expressions that evaluate to colourssg: colouredXThe new model is intended to combine the qualities of the two old models into a single formalism... (p. 166).X(Jensen 1987a), [Jensen 1990]
33(Nelson et al. 1983)1983P/Trf: P/Tsg/l: action, (output) conditional, selectorrf: P/T, sg: inhibit, sg/l: truth-valued expressionsrf: P/TXThese [enhancements, the author] permit the specification of conditional flow and the incorporation of statements to invoke expressions, programs and other nets (p. 590).dsoftware1110.
34(Reis83)1983Relation-NetCP, PrTsg/f: types, capacityXsg/f: multirelationsg: typedXOur central concern is a simple model which allows for a clear and precise description of its behaviour and analysis methods (p. 230).X110.
35(Ajomone Marsan et al. 1984)1984GSPN (Generalized Stochastic Petri Nets)SPN (Molloy)sg: capacitiessg(/l): timed (exponential distribution function), immediatesg: inhibitorXrandom switchnot purely syntactical: A random switch is the set of all enabled immediate transitions together with the associated probability distribution.GSPN are presented and are applied to the performance evaluation of multiprocessor systems (p. 93). No time-related performance measure can be obtained by means of a PN model since time is not considered (p. 94). Often it is not desirable to associate a random time with each transition ... (p. 96).timeXperformance evaluation(Chiola/Ajmone Marsan 1993)11110.
36(Alla et al. 1985)1984CPNrf: CPNrf: CPNrf: CPNrf: CPNXWith each place and transition are associated the same functions.... a FIFO queue may be modelled by means of a coloured Petri net ... (p. 15).g nanananananananananananananananananananananananananananananananananananana
37(Dugan et al. 1984)1984ESPN (Extended Stochastic Petri Nets)SPN (Natkin)rf: P/Tsg: timed (arbitrary distribution function), immediatesg: inhibitor, sg/l: counter, counter-alternate, probabilisticXXThe ESPN model was initially developed as an aid in modeling coverage in fault-tolerant computer systems... [p. 508] ... techniques for the analytic solution of an ESPN ... are explored (p. 507).dXfault tolerant systems111110.
38(Goltz/Reisig 1985)1984CSP-netsPrTrf: PrTrf: PrTrf: PrTsd: program statesXWe define a subclass of predicate/transition-nets and show how to translate CSP-programs into such nets (p. 169).Xnanananananananananananananananananananananananananananananananananananana
39(Lautenbach/Pagnoni 1985)1984Marked-Graph-Like Predicate/Transition NetsPrTsg: unary predicatesg/l: variable 1-tuplesg: constant 1-tupleX(1) predicates have exactly one input and one ouptput arc, (2) pure, (3) strongly connected.... Originally introduced in order to represent certain phenomena related to communication protocols, has turned out to be of theoretical interest (p. 331).dXprotocolsXnanananananananananananananananananananananananananananananananananananana
40(Vautherin/Memmi 1985)1984UP/T (Unary Predicate Transition)PrT, CPNrf: PrTrf: PrT, sg/f: domainrf: PrTsg: 1-tuplesX... such a solution is expensive in time and space, and provides invariants whose meaning is not always clear (p. 456).X110.
41(Voss 1984)1984PrTrf: PrTrf: PrT, sg: macro rf: PrT, sg: readingrf: PrTX... are used to model the second protocol layer of the Local Area Network REDPUC. dprotocols11m10.
42(Corbeel et al. 1986)1985AO nets (Adaptive Petri nets)P/T, self modifyingrf: P/Trf: P/Tsg/l: markin of a place (erasing)rf: P/TXThe net structure changes dynamically by erasing arcs....describing flexible discrete production processes... (p. 162)dmanufacturing110.
43(Molloy 1985)1985Discrete Time Stochastic Petri NetsSPNrf: SPNrf: SPN, sg/l: stochastically timed (geometrically distributed)rf: SPNrf: SPNX... fills the gap between TPN and normal SPN (p. 417).X110.
44(Richter/Voss 1986)1985Channel/Agency (P/T)r: channel, sg/l: resourcer: functionXsg: n-tuples of unstructured objectsproceduresProcedures are associated with functions.On the contrary, an office model should allow to include.... (p. 408)doffice11110.
45(Roucairol 1987)1985FIFO-netsP/Tr: queueXsg/l: words over queue alphabetsg: queue alphabetX... solving generic synchronization problems (p. 436). ... increase of descriptive and computational power (p. 437).synchronization110.
46(Tabak/Levis 1985)1985C/Erf: C/Erf: C/Erf: C/Erf: C/Esd: demimultiplexer The demimultiplexer connects places.The demimultiplexer corresponds to a switch.... is added to represent internal decision making (p. 812).g
47(Zuberek 1986)1985M-Timed Petri NetsTPNrf: P/Tsg/f: firing time (exponentially distributed), firing functionsg: inhibitor, escapeXXImmediate transitions are ordinary ones (without time).... increasing modelling power. ... Petri nets, however, are not complete enough for the study of performance issues since no assumption is made on the duration of systems activities (p. 477).timeperformance evaluation1110., SC
48(Rozenberg/Thiagarajan 1986)1986Elementary Net (EN)Aktionsnetz, C/Er: S-elementsr: T-elementsXXXUsing this model, we shall discuss the fundamental situations ... that can arise in the behaviour of a distributed system (p. 597)... sketch some of the foundational aspects of net theory with the help of this model [Thiagarajan 1987, p. 27].XX[Thiagarajan 1987], (Rosenberg/Engelfriet 1998)
49(Ajmone Marsan/Chiola 1987)1987DSPN (SPN with Deterministic and Exponetial Firing Times)GSPNrf: GSPNrf: GSPN, sg/l: timed (constant)rf: GSPNRXThis work can be considered as a step toward the extension of the class of allowed distributions for continuous-time TTPN (p. 133).time11110.
50(Haddad/Girault 1987)1987Regular NetsCPNrf: CPNrf: CPNrf: CPNrf: CPNX(1) Given two places, then either their colour sets are identical or their colour sets have an empty intersection (p. 77).further restrictions on the incidence matrixColoured nets may be hardly studied...simplify the algebraic structure of the flows space (p. 74). ... restrictions on the incidence matrix.Xnanananananananananananananananananananananananananananananananananananana
51(Oberquelle 1987)1987RFA-nets (role/function/action)r: state, sd: (elementary/complex/storage/common/private) positionr: operation, sg: (elementary/complex) action, activity, function, role, sg/l: automatedr: control flow, sd: object flow, data flowsd: individual control token, individual object tokenspace symbol, coupling symbol(1)The coupling symbol connects operations. (2) The space symbol connects functions/roles/actions. allow to describe socio-technical systems on the function and role level, respectively (p. 180).d socio-technical systems111110.
52(Valk 1987)1987Task-Flow-NetP/T, (higher)rf: P/Trf: P/Trf: P/Tsd: task systemXlater slightly changed and termed Elementary Object Nets... how net theory can be used for modelling task flow in systems of functional units [computer component; the author] (p. 218)d hardware(Valk 1998)
53(Andre 1991)1988Synchronized Elementary Net Systems (SENS)ENrf: ENrf: ENrf: ENrf: ENconstraint structureA constraint structure refers to events or tuples of events. .... had to express timing constraints (p. 2).time110.
54(Battiston et al. 1988)1988OBJSA netshigh-level Petri nets, SA netssg: state-machine components, sg/l: interpretation functionsg/l: objectsg/l: variables, operatorsindividualsXnumber of incoming arcs of a transition = number of outgoing arcs... we aimed to overcome a further weakness which is often ascribed to nets, i.e. the difficulty of structuring them in conformity with the system to be modelled (p. 21).structure1110.
55(Haus/Rodrigueo 1988)1988self-modifying nets, CE+PT, timed netssg: condition, place, sg/f: negatively markedsg: terminal/non-terminal, sg/l: duration (fixed, stochastic/linear probability), sd/l: musical functionssg: bidirectional, labelled (integers), inhibitorsg: control objects, music objectsfeed The feed feature is associated with places or transitions.... this new language allows to explicitly describe and process what we call musical objects (p. 175). dmusic11111110.230.330.170.10N
56(Looney 1988)1988Fuzzy Petri NetsC/Erf: C/Er: neurons, sg/l: decision thresholdsg/l: fuzzy valuesg: fuzzy truth tokenX... to model fuzzy reasoning with propositional logic (p. 178).uncertainty10.
57(Ciardo 1994)1989P/Trf: P/Trf: P/Tsg/l: marking dependent cardinalitiesrf: P/TX... P/T nets with marking dependent arc cardinalities have the potential to express certain system behavior more naturally than ordinary P/T-nets (p. 193).X10.
58(Lipp et al. 1989)1989FPN (Fuzzy Petri-Netz)P/Trf: P/T, sg/l: unscharfsg/l: unscharfrf: P/T, sg/l: unscharfXXEin mehr oder weniger gutes Schalten oder ein Schalten bei nicht ganz exakt erfüllten Bedingungen läßt sich nur mit einem sehr hohen Modellaufwand verwirklichen (S. 12).uncertainty, knowledgeX1i0.
59(Bütler et al. 1990)1990FunPrE-net (predicate/event net with functions)PrT, PN with Objectsr: S-elementsr: T-elements, sg/l: firing function (condition and action)rf: PrTsg: black or typed XThe maximum capacity of S-elements is one.A special form of Predicate/Transition net is used as a model of specification. This allows the realtime simulation of a sufficiently refined specification, which can be used as a system prototype implementation (p. 47). This net class [FunPrE, the author] is sufficiently powerful in describing embedded systems (p. 50).X100.
60(Cardoso et al. 1990)1990Time Fuzzy Petri NetsCooperative Netsrf: PrTrf: PrT, sg/l: authorization function (for uncertain firing)sg/l: object instancessg: object (attribute: duration, location with possibility distribution)Token may be contained in more than one placetime as a token attribute or associated with transitions (as an interval)After having described the importance and complexity of monitoring Flexible Manufacturing Systems, this paper shows the interest of introducing uncertainty and imprecision within Petri net based models (p. 64).uncertaintymanufacturing1m10.
61(Couvreur/Martinez 1990)1990Commutative netsCPNrf: CPNrf: CPNrf: CPNrf: CPNXrestrictions on the colour set. ... the possibilities of analyzing the models are greatly enhanced (p. 148).X0.
62(Huber et al. 1990)1990Hierarchical Coloured Petri NetsCPNrf: CPN sg: substitution, fusionrf: CPN, sg: substitution, fusion, invocationrf: CPNrf: CPNXThe purpose is to break down the complexity of the large model, by dividing it into a number of submodels (p. 314). Hierarchical CP-nets is an attempt to provide the Petri Net modeller with such abstraction mechanisms (p. 315).structure1111i0.160.330.000.00F
63(Chehaibar 1991)1991Reentrant NetCPN, Clean Termination Netsrf: CPN, sg: initial, finalrf: CPNrf: CPNrf: CPNXNet analysis is modular, if... Since our aim is it to obtain such results (p. 59).X(Chehaibar 1993)
64(Ghezzi et al. 1991)1991Time ER nets (Environment/Relationship)High-level PN(sg/l: capacity)sg/l: actionXsg: environments (contains timestamp)XEach environment contains a timestamp variable.... we discuss how time can be modeled (p. 160). time1m010.
65(Hopkins 1991)1991Distributable NetsP/Trf: P/T, sg/f: localityrf: P/T, sg/f: localityrf: P/Trf: P/TX... towards algorithmic generation of a distributed implementation of a net (p. 163).X1110.100.070.330.00
66(Christensen/Petrucci 1992)1992MCPN (Modular CP-nets)CPNrf: CPN, sg: fusion setrf: CPN, sg: fusion setrf: CPNrf: CPNXThey are not intended to be used for practical modelling purposes, but they constitute a formal and general framework for discussing different ways of composing individual CP-nets called modules (p. 113).X1111i0.160.330.000.00F
67(Hanisch 1992)1992Zeitbewertetes NetzP/Trf: P/Trf: P/T, sg/f: Uhrsg/f: Zeitintervallrf: P/TX... werden Petri-Netze als Modellform verwendet, da deren Stärke genau auf dem Gebiet der Modellierung und Analyse von Kopplungen paralleler Abläufe liegt (S. 14). Ein rein kausales Modell kann jedoch die zeitlichen Aspekte der Steuerungsaufgabe .... nicht ausdrücken (S. 112).timeX1110.100.070.330.00
68(Heuser/Richter 1992)1992CPN, Pr/Tsg/l: boundedsg: deadsg: restoring entry/exit arcs, total altering/maintaining entry/exit arcs, sg/l: setsXIsolated constructs are presented.The utility of high-level net classes ... for conceptual modeling of information systems can be considerably increased if the following features are provided ... (p. 241).dsoftware111110.160.330.000.00
69(Anglano/Portinale 1994)1993BNN (Behavioral Petri Net)P/Trf: P/Tsg: OR-transitionsrf: P/Trf: P/TX... intended to model the behavior of a system to be diagnosed (p. 39). ... applicability to diagnostic problem solving (p. 39).ddiagnosis110.
70(Buchholz 1993)1993HGCSPN (Hierarchical Colored Stochastic Petri Nets)GSPN, CPNrf: GSPN, CPN, virtualrf: GSPN, CPN, sg/l: priority, virtualrf: GSPN, CPNrf: GSPN, CPNX... supports the specifications of nets describing large real-world systems. .... can be analyzed extremely efficient (p. 106).XX111111110.260.470.170.00
71(Camargo 1999)1993HHFPN (Hierarchical High Level Fuzzy Petri Nets)PrT, CPNrf: PrTsg/l: operations, sg: substitution nodesg/l: fuzzy objectsg/l: fuzzy objectpagePages are assigned to substitution nodes.The sets of places, transitions and the flow relation of different places are disjoint... the abilty to represent abstractions and refinements as a tool to knowledge based systems design (p. 258)structure 1100.
72(Christensen/Hansen 1993)1993ECPN (Extended CPN)CPNrf: CPN, sg/l: capacity colour setrf: CPNrf: CPN, sg: test, inhibitorrf: CPNXInhibition occurs, when the marking is below a threshold.... improve the possibilities of creating models that are ... compact and comprehensive and .. easy to develop, understand, analyse (p. 186).(X)X11110.
73(David/Alla 1993)1993Timed Continuous Petri Netsrf: P/Tsg/l: firing speedrf: P/Tsg: real numberContinous Petri nets have been introduced by the authors in 1987.When a PN contains a large number of marks, the number of reachable states explodes. This is a practical limitation to the use of Petri nets. Continuous models for discrete systems may provide a very good approximation, this being the basic idea to the definition of continuous Petri nets.XX1110.100.070.330.00
74(Fehling 1993)1993Hierarchical Petri NetsC/Erf: C/Erf: C/Erf: C/Erf: C/Eroot (graphs)Nodes are connected to nodes or to the root.... facilitate the modeling of large real-world systems, rather than using them for theoretical considerations (p. 148).X110.
75(Souissi 1993)1993DSSP (Deterministic Systems of sequential processes)P/Trf: P/T, sg: bufferrf: P/Trf: P/Trf: P/TX(1) subnet is a state machine, (2) further restrictions (e.g. on buffers).. our first aim is to give efficient and formal methods for the validation ... (p. 406).X110.
76(Trivedi/Kulkarni 1993)1993FSPN (Fluid Stochastic Petri Nets)sg/l: discrete, continuoussg: timed (exponentially distributed), immediatesg/l: discrete, fluidsg: fluidXNo arcs are allowed between continuous places and immediate transitions.... to handle stochastic fluid flow systems (p. 24).dstochastic fluid systems1110.100.070.330.00
77(van der Aalst 1993)1993ITCPN (Interval Timed Coloured Petri Net)CPNsg: CPNrf: CPNrf: CPNrf: CPN (timestamp)XThe transition with the smallest enabling time will fire first, the produced tokens have a delay.... only timed AND coloured Petri nets are capable of modeling large and complex real-time systems (p. 453).X1m110.130.130.330.00
78(Buchholz 1994)1994HHPN (Hierarchical High Level Petri Nets)CP-nets (= HPN)rf: CPNrf: CPNrf: CPNrf: CPNaggregated viewAggregated views receive input from transitions and produce output to places.Apart from specification convenience HHPNs can be analysed very efficiently ... (p. 119). XX111110.160.330.000.00
79(Christensen/Hansen 1994)1994CCPNCP-netsrf: CPNrf: CPN, sg/l: communicationrf: CPNrf: CPNchannel (CSP, programming language)Channels connect communication transitions.... include constructs making it easy to model synchronisation and synchronous communication (p. 160). synchronization1110.
80(Diaz/Sénac 1994)1994TSPN (Time Stream Petri Nets)Timed Petri netsrf: P/Tsg/f: typing (firing: strong, weak, and, or, master)sg/f: temporal validity intervalXThis paper introduces a model for specifying synchronization constraints in distributed asynchronous multimedia systems and applications (p. 219). TStreamPN allow the timed behavior of streams to be fully, accurately and formally described (p. 219). TStreamPNs are proposed to precisely model the complex behaviour of synchonized multimedia streams (p. 219).synchronization, timemultimedia1010.
81(Donatelli 1994)1994SGSPN (Superposed Generalized Stochastic Petri Nets)GSPNrf: GSPNrf: GSPN, sg/l: synchronizedrf: GSPNrf: GSPNXA GSPN is a set of GSPN that synchronize on a common subset of transitions of equal rate.... the major draw-back of Stochastic Petri Nets (SPN) and their generalisation GSPN is the large state space that can be generated even by rather simple models (p. 258).X111110.
82(Lakos/Christensen 1994)1994ECPNrf: ECPNrf: ECPNrf: ECPN, sg/l: projectedrf: ECPNXIt is general because ... it encompasses the other proposals for arc extensions ... (p. 338).X111110.160.330.000.00
83(Pedrycz/Peters 1999)1994GFPN (Generalized Fuzzy Petri Nets)CPNrf: CPNrf: CPNrf: CPN, sg/f: strenght of connection, reference pointsrf: CPNX... were introduced to model processes in reasoning systems and, in particular, logic processing where computations are performed in the context of fuzzy sets ... (p. 276)uncertaintyknowledge based reaoning110.
84(Sibertin-Blanc 1994)1994Cooperative NetsHigh-Levelsg: accept, return, sg/f: typesg/l: function, action, sg: request, retrievesg/l: tuples of variablessg: tuple of constants or object names of typesX... has a high expressive power and on the other hand has strong theoretical basis. By a high expressive power we intend the possibility to model complex distibuted systems made up of a number of entities which have their own internal structure and behavior, and also interact the ones with the others (p. 471).g 11110.
85(Barkaoui et al. 1995)1995Extended Non Self-Controlling NetsP/T, Extended Free-Choice-Nets, Non Non Self-Controlling Netsrf: P/Trf: P/Trf: P/Trf: P/TX(1) If two places share postset transitions, the postsets are identical. (2) For every couple (a, b) of transitions in conflict, there does not exist a conflict-free path leading from a to b.... a new class of P/T nets for which the deadlock-trap property is a sufficient liveness condition (p. 25).Xnanananananananananananananananananananananananananananananananananananana
86(Best et al. 1995)1995M-nets (multilabeled)Pr/Trf: Pr/T, sg/l: status (entry, exit, internal)rf: Pr/T, sg/l: communication interfacerf: Pr/Trf: Pr/TX(1) There is always at least one entry and one exit place.... allow the modular construction of large high-level nets from smaller components (p. 102).X[Benzaken et al. 1998]111110.160.330.000.00
87(Haddad/Poitrenaud 1999)1995RPN (Recursive Petri nets)P/Trf: P/Tsg: elementary, abstract, finalrf: P/Trf: P/TXThe model of recursive Petri nets (RPNs) has been introduced in the field of multi-agents systems in order to model flexible plans for agents (p. 228).multi-agent systemsi1iii0.160.330.000.00RCA
88(Lakos 1995)1995Object Petri NetsMCPN, CCPNrf: MCPN, super, portrf: MCPN, superrf: MCPN, sg: inhibitor, testrf: MCPNX(1) each transition has at most one input/output arc, (2) at most one inhibitor/test arc for each place-transition pair... by proposing a complete integration of object-oriented concepts ... into the Petri net formalism (p. 278).object orientation 111111m0.230.470.000.00
89(Schöf et al. 1995)1995THOR-nets (Timed Hierarchical Object-Related)High-levelsg: structured (multiset, stack, queue), sg/f: capacitysg/l: activation condition, action block, delay, firing time, firing capacity, refinedsg: enabling, inhibitor, consuming, sg/l: weightedsg: objects (OO programming)XThe aim is ... to develop and implement an efficient modeling technique and methods for a fast sequential and distributed simulation of real-time systems ... (p. 412).X1110111110.260.400.330.00S, SC
90(Sénac et al. 1995)1995HTSPN (Hierarchical Time Stream Petri Nets)TSPN (Time Stream Petri Nets)sd/f: type (atomic = monomedia, composite = multimedia scenario, link type = hypermedia)rf: TSPNrf: TSPNrf: TSPNX... for the specification of temporal constraints and description of logical behaviour in distributed hypermedia systems (p. 451).dhypermedia1101110.
91(Colom 2003)1995P/Tsd/l: process, idle, resource, capacityrf: P/Trf: P/Trf: P/TXself-loop freeThe formulation of this application-driven problem [Flexible Manufacturing Systems, the author] in terms of Petri nets leads to a class of models... (p. 23).manufacturing(Ezpeleta et al. 1995)1110.
92(Horton 1998)1996FSPN (Fluid Stochastic Petri Nets)GSPNrf: GSPN, sg: fluidrf: GSPNrf: GSPN, sg: fluid, sg/f: raterf: GSPN, sg: fluidXFluid flows connect only fluid places and timed transitions.... [FSPSN]... eine Möglichkeit zur Modellierung diskret-kontinuierlicher Systeme bereitstellen...(S. 17) ... fassen bereits bekannte Zusatztechniken in einem Formalismus zusammen (S. 17).dXdiscrete-continuous systems1111110.190.270.330.00
93(Kindler/Walter 1996)1996Arc-typed netshigh-level netsrf: PrTsg/f: labelsg/l: multiset of terms, sg: arc typessg: elements from the set of all multisets over an algebraX. ... provide an adequate level of abstraction for these kinds of applications [communication protocols, the author] (p. 289).structureprotocols[Kindler 2002]
94(Murata et al. 1999)1996FTHN (Fuzzy-Timing High Level PN)CPNrf: CPNrf: CPNrf: CPN, sg/l: fuzzy delayrf: CPN (fuzzy timestamp)X... to include the explicit notion of time in nets so as not to violate Petri's recently proposed axioms on nets (p. 88).time1m110.130.130.330.00
95(Recalde et al. 1996)1996{SC}*ECSP/Trf: P/T, sg: bufferrf: P/Trf: P/Trf: P/TX(1) if transitions share a preset, it is identical (equal conflict), (2) restrictions on buffersMaybe, because of a disjoint union, buffers are not seen as places. The formulation of the disjoint union is somewhat unclear.After defining the class [{SC]*ECS, the author], we take advantage of its modular and hierarchical structure to analyse it (p. 440). ... they keep (part of) their tractability (p. 441).Xnanananananananananananananananananananananananananananananananananananana
96(Bruni/Montanari 2000)1997Zero-safe netsP/Trf: P/T, sg: zero-placesrf: P/Trf: P/Trf: P/TXzero-safe nets, which extend PT nets with a simple mechanism for transition synchronization (p. 83).synchronization110.
97(Kindler 1997)1997P/Trf: P/T, sg: input, outputsg: qiescent, progressrf: P/Trf: P/TX... provides a semantical foundation for a modular verification method (p. 236). X11i0.
98(Kishinevsky et al. 1997)1997PCN (Place Chart Nets)P/Tr: place chartsg: preemptivesg: preemptingrf: P/TXPreempting arcs remove all tokens, preemtive place charts abort the search.The original Petri net model, unfortunately, lacks a notion of hierarchy (p. 329).structure11ii0.
99(van der Aalst 1997)1997WF-nets (WorkFlow nets)P/Trf: P/T, sg: source, sinkrf: P/Trf: P/Trf: P/TXThe preset of source places and the postset of sink places are empty. (2) Every WF-net has one input place and one output place.... representation, validation and verification of workflow procedures (p. 407).dXworkflow
100(Franceschinis/Ribaudo 1998)1998SWN (Stochastic Wellformed Net)GSPN, CPNrf: CPNsg: timed (exponential distribution function), immediate, sg/f: weight, sg/l: guardsg: inhibitor, sg/l: weighted sum of guarded tuplesrf: CPNX... (SWNs), a high level SPN formalism in which behavioral symmetries can be automatically discovered and exploited (p. 387) ...X1m1110.
101(Kindler/Völzer 1998)1998Algebraic system netsg: sortedsg/l: guardsg: flexiblesg: SIG-terms of some sortX... lack a feature for modeling distributed network algortihms, viz. flexible arcs (p. 345). .. are better suited for modeling distributed algorithms (p. 345).d algorithms1110.
102(Bastide et al. 1999)1999CO (Coperative Objects)CPNsg/l: token typesg/l: precondition, actionsg/l: tuples of variables, multiplicity), sg: test, inhibitorsg: tuples of typed valuesX... aims at providing a suitable solution to the problem of behavioural specification of distributed objects, in the context of CORBA (p. 67).d object orientation111110.160.330.000.00
103(Fanchon 1999)1999Trace Channel netsCPN, FIFOr: channelrf: CPNsg/l: traces sg: tracesXTrace Channel Nets can be comprehensively seen as a 'natural' generalization of existing classes of nets (p. 305).Xnanananananananananananananananananananananananananananananananananananana
104(Recalde et al. 1996)1999Autonomous Continuous P/T SystemsP/Trf: P/Trf: P/Trf: P/Tsg: fluidXDiscrete event dynamic systems may have extremely large state spaces. For their analysis, it is usual... Applying this idea, continuous P/T systems are defined ... (p. 107).X110.
105(Schneider/Wehler 1999)1999Artin netsCPNrf: CPNrf: CPNrf: CPNrf: CPNXrestrictions on the colour sets of places and transitionsWe introduce Artin nets a subclass of coloured nets, which can be handled by methods from commutative Algebra (p. 248).Xnanananananananananananananananananananananananananananananananananananana
106(Ballarini et al. 2000)2000Parametric Stochastic Well-Formed NetsStochastic Well-Formed Netssg: coloured (cartesian product of basic color classes)sg: coloured, guards, priority, labeled (import/export functions)sg: labeled (variables typed by colour, arithmetic expressions), inhibitorsg: elements from a basic or parametric colour classX... in order to increase modularity and reuse of the modelling efforts (p. 43).X10.
107(Vogler 2000)2000Petri Nets with Time Bounds and InterfaceP/Trf: P/T, sg: input, outputsg/f: time bounds {0, 1}XXXunknown------11110.130.130.330.00
108(Deussen 2001)2001RN (Register Net)ENrf: ENsg/l: predicates, sg/f: register treatment rf: EN, readingsg: value from a registerregisterRegister can be associated to transitions as input or output.We address the verification of programmable logic controllers (p.144). RN's represent the control flow of an IL [instruction list, the author]... by means of a Petri net ... (p. 144).dXhardware11110.
109(Köhler et al. 2001)2001Reference NetsCPNrf: CPNrf: CPN, sg: reservation, test, inhibitorsg: object netsynchronous channelsChannels connect one transition to exactly one other for one occurrence.Reservation arcs reserve tokens for a transition.unknown----(Köhler 2004)1110.
110(Nielsen et al. 2001)2001Distributed Timed-Arc Petri Nets(Zeitbehaftetes Netz)(sg: capacity)rf: P/Tsg/f: time intervalssg/l: agesynchronization relationThe synchronization relation is defined on at least two places.... allowing a local timing as well as distributed time synchronization (p. 23). time, synchronization1m010.
111(Di Marzo Serugendo et al. 2002)2002Real-Time Synchronized Petri-netssg/f: capacitysg: methods, sg/l: time intervalsg: inhibitorsg: time stampedsynchronization expressionMethods and Transitions may request synchronization with methods.Our proposal enables one to define complex systems with compact specifications ... (p. 142)X11110.
112(Stork/van Glabbeek 2002)2002PrTrf: PrT, sg: refinement (guarded), input, outputrf: PrTrf: PrTsg: structuredX.... Petri net theory as is stands is incapable of expressing properties we seek in such extended workflows (p. 395).dworkflow11m10.
113(Fleischhack/Pelz 2003)2003Hierarchical Duration M-netsTimed M-nets, CPNsg: labeled (type, status)sg/l: communication (labeled by guard, action, range for duration), hierarchical (labeled by hierarchical actions)rf: CPNrf: CPNRefined nets can be associated with transitions....which is shown to be a powerful feature for abstraction (p. 397). We would like to embody .. a global time constraint (p. 398).structure, time011a10.130.130.330.00
114(Genc/Lafortune 2003)2003(P/T?)rf: P/Tsg/l: observable/unobservable fault eventssg/l: weightsg: {0, 1}, typesX.... where some of the transitions are labeled by different fault events (p. 317).d(X)fault tolerant systems110.
115(Matsuno et al. 2003)2003HFBN (Hybrid functional Petri net)Hybrid PNsg: discrete, continuoussg: discrete, continuous, sg/l: functionsg/l: weight, inhibitory, test, functionsg: integer, real valuesXFuntional continuous transitions control the speed/condition of consumption/production/firing.... an extension ... which allows us to model biopathways naturally and efficiently (p. 3).dbiology11110.
Copyright(a) Susanne Patig, 2005