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Adapted  Included  Adapted  Included 
1  (Petri 1962)  1962  ANetz   X  X, (r: Aktion)  X  r: 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                                       0.00  0.00  0.00  0.00   
1+  (Holt 1968)  1968  PetriNet (C/ENet: Condition/Event)   X  X  r: input/putput relations  X      (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]                                 0.00  0.00  0.00  0.00   
2  (Genrich 1969)  1969  Synchronisationsgraph   r: Kanten  r: Knoten  (X)  r: Marke      X  Each "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]  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
3a  (Holt/Commoner 1970)  1970  Marked Graph  C/E  X  X  X  X      X  Each 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).   X                                      0.00  0.00  0.00  0.00   
3b  (Holt/Commoner 1970)  1970  State Machine Graph  C/E  X  X  X  X      X  Each transition has at most one input place and at most one output place.   see above; not counted               na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
4  (Patil 1970)  1970  Coordination Net  C/E  X  sg: input, output, internal  X  r: stone  constraint 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).    X          1    1                         0.06  0.13  0.00  0.00   
5  (Hack 1972)  1972  Free Choice Net  P/T  X  X  X  X      X  Every 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).   X       na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
6  (Nutt 1972a)  1972  ENets (Evaluation Net)  C/E  r: location, sg: peripheral, resolution  sg/l: type (T,F, J, X, Ytransition), sg/f: transition time  X  sg: attribute token      X  (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).  time  X    performance evaluation   (Nutt 1972b)    1      1    1  1         1             0.16  0.27  0.17  0.00   
7  (Agerwala/Flynn 1973)  1973   P/T  sg: 'contrary'  sg: ORinput  sg: inhibitor       X   A 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).  coodination           1     1     1                     0.10  0.20  0.00  0.00   
8  (Baer 1973a)  1973    rf: P/T, sg: switch  rf: P/T, XORtransition  rf: P/T, sg: absorber  rf: P/T      X  (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).  d     algorithms   (Baer 1973a)         1     1  1                    0.10  0.20  0.00  0.00   
9  (Noe/Nutt 1973)  1973  Macro ENets  ENets  rf: ENets, sg: macro location (Q)  rf: ENets, sg: macro transition (X, Y, A, RH)  rf: Enets  rf: Enets      X   The Xtransition 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).    X      1  1  1      1    1  1         1             0.23  0.40  0.17  0.00  S  
10  (Ramachandi 1973)  1973  TPN (Timed Petri Nets)  P/T  rf: P/T  sg/f: firing time  X  X      X    This [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. 910). ... motivated by the desire to study performance issues .... (p. 10).  time     performance evaluation       m                  1            0.06  0.07  0.17  0.00   
11  (Fuss 1975)  1974  PTNetze (Puffer/Transition)  P/T  r: Puffer, sg: Steuer  r: Transaktoren  rf: P/T  rf: P/T      X    ... ergab sich aus dem Abwägen der praktischen Belange... (p. 326)    X         1    1                          0.06  0.13  0.00  0.00   
12  (Noe 1980a)  1975  ProNet  ENets  sg/l: bounds  sg/l: procedure, firing delays (interval)  sg: ANDlogic, selector  rf: Enet  global 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).  structure     performance evaluation      1  1     1    1  1         1             0.19  0.33  0.17  0.00   
13  (Merlin/Farber 1976)  1976  TPN (Time Petri Net)  C/E  X  sg/l: firing delay interval  X  X      X    .... 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     protocols                       1             0.03  0.00  0.17  0.00   
14  (Symons 1980)  1976  NPN (Numerical Petri Net)  P/T   sg/f: operation  sg/l: enabling condition  sg/l: values  memory     Transitions 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).  d     protocols      1  1  1      1                       0.13  0.27  0.00  0.00   
15  (Sifakis 1980)  1977  TPTN (Timed PlaceTransition Nets)  P/T (, TPN)  rf: P/T, sg/f: time base  rf: P/T  rf: P/T  rf: P/T, sg: available/unavailable      X    The use of asynchronous models for performance evaluation necessitates that they be augmented by introducing a time parameter ... (p. 307).  time     performance evaluation      1  1                1              0.10  0.13  0.17  0.00   
16  (Valette 1977)  1977  Control Graph  P/T  sg: idle  sg/l: logical function, operators        X  The 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  X          1  1      1                       0.10  0.20  0.00  0.00   
17  (Genrich/Lautenbach 1978)  1978  P/T (Place/Transition)   sg: capacities  X  sg/f: weighted  X      X    unknown                                              0.00  0.00  0.00  0.00   
18  (Moalla et al. 1978)  1978  SPN (Synchronized Petri Nets)  P/T  rf: P/T  rf: P/T  rf: P/T  rf: P/T  event     (1) Events are assigned to transitions.    .... (SPN) which permit the description of synchronous nonautonomous systems (p. 375).  sychronization, nonautonomy           m       1      0                  0.06  0.13  0.00  0.00   
19  (Schiffers/Wedde 1978)  1978  CPNets (Coloured PetriNets)  P/T  rf: P/T  rf: P/T  rf: P/T  sg: coloured      X  Each source place is assigned exactly one target place through a transition (stream).   .. for describing the process structure ... (p. 463).  structure          i  1            i                  0.10  0.20  0.00  0.00  ST  
20  (Valk 1978a)  1978  SelfModifying Nets  P/T  rf: P/T  rf: P/T  sg/l: marked places  rf: P/T      X    We now introduce an extension, called selfmodifying nets, which includes the previous ones (p. 526).     X    (Valk 1978b)     1    1                          0.06  0.13  0.00  0.00   
21  (Genrich/Lautenbach 1981)  1979  PrT (Predicate/Transition)  C/E, P/T  sg: predicates, sg/f: capacity  sg/l: logical formulas, sg: dead  sg/l: formal sums  sg: items (ntupels of individual symbols)      X    Our 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).  individuals          1  1   m                           0.10  0.20  0.00  0.00   
22  (Oberquelle 1980)  1979  CAnets (Channel/Agency nets); MAnets (Means/Activities)   sd: channel, means  sd: agency, activities  sd: takes/puts, necessary/result  sd: message         ... new interpretations arising from teaching necessities (p. 483), ... representation (p. 481).  d     teaching                         1           0.03  0.00  0.00  0.10   
23  (Shapiro 1979a)  1979  RPN (Random Petri Net)  C/E  rf: C/E  rf: C/E  sg: random switch  rf: C/E      X    ... 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).  uncertainty     fault tolerant systems          i                          0.03  0.07  0.00  0.00  RS  
24  (Shapiro 1979b)  1979   C/E  sd: complex condition  sd: activity, violations, sg: fact  rf: C/E  rf: C/E  transmission     A transmission passes through an activity and connects complex conditions.    ... facilitate the design and construction of information systems ... (p. 107)  d     software         1         1                 1   0.10  0.13  0.00  0.10   
25  (Florin/Natkin 1982)  1980  SPN (Stochastic Petri Nets)  P/T  rf: P/T  sg/l: stochastically delayed (arbitrary distribution function)  X  X      X    unknown                  1                 1             0.06  0.07  0.17  0.00   
26  (Hinderer 1982)  1980  Anets (Algebraic nets)  C/E  X  sd/l: polynomial semiring  X  X      X    ... they [Anets, the author] are designed to the purpose of categorical considerations (p. 142).  d     mathematics                                   0.00  0.00  0.00  0.00   
27  (Yoeli 1982)  1980  Extended Petri Nets  P/T  rf: P/T  sg/f: condition function, action function  X  X      X    ... is a powerful and convenient tool for the formal specification of .. cooperating sequential processes and communication protocols (p. 183).  d     protocols        1     1                        0.06  0.13  0.00  0.00   
28  (De Cindio et al. 1982)  1981  SA nets (Superposed Automata)  PrT  rf: PrT  rf: PrT  rf: PrT  rf: PrT      X  number of incoming arc of a transition = number of outgoing arcs   ... to support system verification and evaluation (p. 269)   X      [De Cindio et al. 1987]  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
29  (Molloy 1982)  1981  SPN (Stochastic Petri Nets)  P/T  rf: P/T  sg/l: transition rate (exponentially distributed firing time)  X  X      X    ... [existing approaches, the author] have omitted any study of timing considerations. ... include timing as a specification (p. 914).  time           1                 1             0.06  0.07  0.17  0.00   
30  (Jensen 1981)  1981  CP81Nets (Coloured Petri nets)  PrT  sg/f: colour set  sg/f: colour set  sg/l: functions denoting formal sums  sg: coloured      X    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)    1  1                             0.06  0.13  0.00  0.00   
31  (Coolahan/Roussopoulos 1983)  1983   TPN, P/T  rf: P/T, sg/l: execution time  sg: immediate  X  X      X    ... an extension to the classic Petri net definition to incorporate the notion of time (p. 604).  time           m                1  1             0.10  0.07  0.33  0.00   
32  (Jensen 1983)  1983  CPN (Coloured Petri nets)  CP81nets, PrT  sg/f: colour set  sg/f: colour set, sg/f: guard  sg/l: expressions that evaluate to colours  sg: coloured      X    The new model is intended to combine the qualities of the two old models into a single formalism... (p. 166).     X    (Jensen 1987a), [Jensen 1990]    1  1                             0.06  0.13  0.00  0.00   
33  (Nelson et al. 1983)  1983   P/T  rf: P/T  sg/l: action, (output) conditional, selector  rf: P/T, sg: inhibit, sg/l: truthvalued expressions  rf: P/T      X    These [enhancements, the author] permit the specification of conditional flow and the incorporation of statements to invoke expressions, programs and other nets (p. 590).  d     software        1    1     1                     0.10  0.20  0.00  0.00   
34  (Reis83)  1983  RelationNet  CP, PrT  sg/f: types, capacity  X  sg/f: multirelation  sg: typed      X    Our central concern is a simple model which allows for a clear and precise description of its behaviour and analysis methods (p. 230).    X        1  1                             0.06  0.13  0.00  0.00   
35  (Ajomone Marsan et al. 1984)  1984  GSPN (Generalized Stochastic Petri Nets)  SPN (Molloy)  sg: capacities  sg(/l): timed (exponential distribution function), immediate  sg: inhibitor  X  random switch     not 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 timerelated 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).  time  X    performance evaluation   (Chiola/Ajmone Marsan 1993)     1     1       1       1             0.13  0.20  0.17  0.00   
36  (Alla et al. 1985)  1984   CPN  rf: CPN  rf: CPN  rf: CPN  rf: CPN      X  With 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        na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
37  (Dugan et al. 1984)  1984  ESPN (Extended Stochastic Petri Nets)  SPN (Natkin)  rf: P/T  sg: timed (arbitrary distribution function), immediate  sg: inhibitor, sg/l: counter, counteralternate, probabilistic  X      X    The ESPN model was initially developed as an aid in modeling coverage in faulttolerant computer systems... [p. 508] ... techniques for the analytic solution of an ESPN ... are explored (p. 507).  d  X    fault tolerant systems       1    1  1     1         1             0.16  0.27  0.17  0.00   
38  (Goltz/Reisig 1985)  1984  CSPnets  PrT  rf: PrT  rf: PrT  rf: PrT  sd: program states      X    We define a subclass of predicate/transitionnets and show how to translate CSPprograms into such nets (p. 169).       X   na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
39  (Lautenbach/Pagnoni 1985)  1984  MarkedGraphLike Predicate/Transition Nets  PrT  sg: unary predicate   sg/l: variable 1tuple  sg: constant 1tuple      X  (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).  d  X    protocols  X   na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
40  (Vautherin/Memmi 1985)  1984  UP/T (Unary Predicate Transition)  PrT, CPN  rf: PrT  rf: PrT, sg/f: domain  rf: PrT  sg: 1tuples      X    ... such a solution is expensive in time and space, and provides invariants whose meaning is not always clear (p. 456).   X         1  1                             0.06  0.13  0.00  0.00   
41  (Voss 1984)  1984   PrT  rf: PrT  rf: PrT, sg: macro  rf: PrT, sg: reading  rf: PrT      X    ... are used to model the second protocol layer of the Local Area Network REDPUC.  d     protocols     1  1  m         1                     0.13  0.27  0.00  0.00   
42  (Corbeel et al. 1986)  1985  AO nets (Adaptive Petri nets)  P/T, self modifying  rf: P/T  rf: P/T  sg/l: markin of a place (erasing)  rf: P/T      X   The net structure changes dynamically by erasing arcs.  ...describing flexible discrete production processes... (p. 162)  d     manufacturing       1    1                          0.06  0.13  0.00  0.00   
43  (Molloy 1985)  1985  Discrete Time Stochastic Petri Nets  SPN  rf: SPN  rf: SPN, sg/l: stochastically timed (geometrically distributed)  rf: SPN  rf: SPN      X    ... fills the gap between TPN and normal SPN (p. 417).     X        1                 1             0.06  0.07  0.17  0.00   
44  (Richter/Voss 1986)  1985   Channel/Agency (P/T)  r: channel, sg/l: resource  r: function  X  sg: ntuples of unstructured objects  procedures     Procedures are associated with functions.    On the contrary, an office model should allow to include.... (p. 408)  d     office     1  1  1                    1          0.13  0.20  0.00  0.10   
45  (Roucairol 1987)  1985  FIFOnets  P/T  r: queue  X  sg/l: words over queue alphabet  sg: queue alphabet      X    ... solving generic synchronization problems (p. 436). ... increase of descriptive and computational power (p. 437).  synchronization          1  1                             0.06  0.13  0.00  0.00  S  
46  (Tabak/Levis 1985)  1985   C/E  rf: C/E  rf: C/E  rf: C/E  rf: C/E  sd: demimultiplexer     The demimultiplexer connects places.   The demimultiplexer corresponds to a switch.  ... is added to represent internal decision making (p. 812).  g                   1                     0.03  0.07  0.00  0.00   
47  (Zuberek 1986)  1985  MTimed Petri Nets  TPN  rf: P/T  sg/f: firing time (exponentially distributed), firing function  sg: inhibitor, escape  X      X   Immediate 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).  time     performance evaluation       1     1              1            0.10  0.13  0.17  0.00  I, SC  
48  (Rozenberg/Thiagarajan 1986)  1986  Elementary Net (EN)  Aktionsnetz, C/E  r: Selements  r: Telements  X  X      X    Using 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].     X   X  [Thiagarajan 1987], (Rosenberg/Engelfriet 1998)                                 0.00  0.00  0.00  0.00   
49  (Ajmone Marsan/Chiola 1987)  1987  DSPN (SPN with Deterministic and Exponetial Firing Times)  GSPN  rf: GSPN  rf: GSPN, sg/l: timed (constant)  rf: GSPN  R      X    This work can be considered as a step toward the extension of the class of allowed distributions for continuoustime TTPN (p. 133).  time           1     1       1       1             0.13  0.20  0.17  0.00   
50  (Haddad/Girault 1987)  1987  Regular Nets  CPN  rf: CPN  rf: CPN  rf: CPN  rf: CPN      X  (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 matrix  Coloured nets may be hardly studied...simplify the algebraic structure of the flows space (p. 74). ... restrictions on the incidence matrix.   X       na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
51  (Oberquelle 1987)  1987  RFAnets (role/function/action)   r: state, sd: (elementary/complex/storage/common/private) position  r: operation, sg: (elementary/complex) action, activity, function, role, sg/l: automated  r: control flow, sd: object flow, data flow  sd: individual control token, individual object token  space symbol, coupling symbol     (1)The coupling symbol connects operations. (2) The space symbol connects functions/roles/actions.    allow to describe sociotechnical systems on the function and role level, respectively (p. 180).  d     sociotechnical systems    1  1  1                      1        1  0.16  0.20  0.00  0.20   
52  (Valk 1987)  1987  TaskFlowNet  P/T, (higher)  rf: P/T  rf: P/T  rf: P/T  sd: task system      X   later 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)    1  1                             0.06  0.13  0.00  0.00   
53  (Andre 1991)  1988  Synchronized Elementary Net Systems (SENS)  EN  rf: EN  rf: EN  rf: EN  rf: EN  constraint structure     A constraint structure refers to events or tuples of events.    .... had to express timing constraints (p. 2).  time                     1      1              0.06  0.07  0.17  0.00   
54  (Battiston et al. 1988)  1988  OBJSA nets  highlevel Petri nets, SA nets  sg: statemachine components, sg/l: interpretation function  sg/l: object  sg/l: variables, operators  individuals      X  number 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).  structure        1   1  1                             0.10  0.20  0.00  0.00   
55  (Haus/Rodrigueo 1988)  1988   selfmodifying nets, CE+PT, timed nets  sg: condition, place, sg/f: negatively marked  sg: terminal/nonterminal, sg/l: duration (fixed, stochastic/linear probability), sd/l: musical functions  sg: bidirectional, labelled (integers), inhibitor  sg: control objects, music objects  feed     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).  d     music     1   1    1  1    1          1          1    0.23  0.33  0.17  0.10  N  
56  (Looney 1988)  1988  Fuzzy Petri Nets  C/E  rf: C/E  r: neurons, sg/l: decision threshold  sg/l: fuzzy value  sg: fuzzy truth token      X    ... to model fuzzy reasoning with propositional logic (p. 178).  uncertainty          1                              0.03  0.07  0.00  0.00  Z  
57  (Ciardo 1994)  1989   P/T  rf: P/T  rf: P/T  sg/l: marking dependent cardinalities  rf: P/T      X    ... P/T nets with marking dependent arc cardinalities have the potential to express certain system behavior more naturally than ordinary P/Tnets (p. 193).    X            1                          0.03  0.07  0.00  0.00   
58  (Lipp et al. 1989)  1989  FPN (Fuzzy PetriNetz)  P/T  rf: P/T, sg/l: unscharf  sg/l: unscharf  rf: P/T, sg/l: unscharf  X      X    Ein 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, knowledge   X         1    i                          0.06  0.13  0.00  0.00  Z  
59  (Bütler et al. 1990)  1990  FunPrEnet (predicate/event net with functions)  PrT, PN with Objects  r: Selements  r: Telements, sg/l: firing function (condition and action)  rf: PrT  sg: black or typed      X   The maximum capacity of Selements 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).   X         1  0                             0.03  0.07  0.00  0.00   
60  (Cardoso et al. 1990)  1990  Time Fuzzy Petri Nets  Cooperative Nets  rf: PrT  rf: PrT, sg/l: authorization function (for uncertain firing)  sg/l: object instances  sg: object (attribute: duration, location with possibility distribution)      Token may be contained in more than one place   time 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).  uncertainty     manufacturing      1  m                 1             0.10  0.13  0.17  0.00   
61  (Couvreur/Martinez 1990)  1990  Commutative nets  CPN  rf: CPN  rf: CPN  rf: CPN  rf: CPN      X  restrictions on the colour set.   ... the possibilities of analyzing the models are greatly enhanced (p. 148).   X                                      0.00  0.00  0.00  0.00   
62  (Huber et al. 1990)  1990  Hierarchical Coloured Petri Nets  CPN  rf: CPN sg: substitution, fusion  rf: CPN, sg: substitution, fusion, invocation  rf: CPN  rf: CPN      X    The purpose is to break down the complexity of the large model, by dividing it into a number of submodels (p. 314). Hierarchical CPnets is an attempt to provide the Petri Net modeller with such abstraction mechanisms (p. 315).  structure        1  1  1  1            i                  0.16  0.33  0.00  0.00   F 
63  (Chehaibar 1991)  1991  Reentrant Net  CPN, Clean Termination Nets  rf: CPN, sg: initial, final  rf: CPN  rf: CPN  rf: CPN      X    Net analysis is modular, if... Since our aim is it to obtain such results (p. 59).   X      (Chehaibar 1993)    1  1                             0.06  0.13  0.00  0.00   
64  (Ghezzi et al. 1991)  1991  Time ER nets (Environment/Relationship)  Highlevel PN  (sg/l: capacity)  sg/l: action  X  sg: environments (contains timestamp)      X   Each environment contains a timestamp variable.  ... we discuss how time can be modeled (p. 160).  time          1  m  0               1              0.10  0.13  0.17  0.00   
65  (Hopkins 1991)  1991  Distributable Nets  P/T  rf: P/T, sg/f: locality  rf: P/T, sg/f: locality  rf: P/T  rf: P/T      X    ... towards algorithmic generation of a distributed implementation of a net (p. 163).       X      1              1  1               0.10  0.07  0.33  0.00   
66  (Christensen/Petrucci 1992)  1992  MCPN (Modular CPnets)  CPN  rf: CPN, sg: fusion set  rf: CPN, sg: fusion set  rf: CPN  rf: CPN      X    They 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 CPnets called modules (p. 113).     X     1  1  1  1            i                  0.16  0.33  0.00  0.00   F 
67  (Hanisch 1992)  1992  Zeitbewertetes Netz  P/T  rf: P/T  rf: P/T, sg/f: Uhr  sg/f: Zeitintervall  rf: P/T      X    ... werden PetriNetze 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).  time  X          1                1  1             0.10  0.07  0.33  0.00   
68  (Heuser/Richter 1992)  1992   CPN, Pr/T  sg/l: bounded  sg: dead  sg: restoring entry/exit arcs, total altering/maintaining entry/exit arcs, sg/l: sets       X   Isolated constructs are presented.  The utility of highlevel net classes ... for conceptual modeling of information systems can be considerably increased if the following features are provided ... (p. 241).  d     software       1   1  1  1     1                     0.16  0.33  0.00  0.00   
69  (Anglano/Portinale 1994)  1993  BNN (Behavioral Petri Net)  P/T  rf: P/T  sg: ORtransitions  rf: P/T  rf: P/T      X    ... intended to model the behavior of a system to be diagnosed (p. 39). ... applicability to diagnostic problem solving (p. 39).  d     diagnosis       1     1                         0.06  0.13  0.00  0.00   
70  (Buchholz 1993)  1993  HGCSPN (Hierarchical Colored Stochastic Petri Nets)  GSPN, CPN  rf: GSPN, CPN, virtual  rf: GSPN, CPN, sg/l: priority, virtual  rf: GSPN, CPN  rf: GSPN, CPN      X    ... supports the specifications of nets describing large realworld systems. .... can be analyzed extremely efficient (p. 106).   X  X      1  1  1  1     1     1   1       1             0.26  0.47  0.17  0.00   
71  (Camargo 1999)  1993  HHFPN (Hierarchical High Level Fuzzy Petri Nets)  PrT, CPN  rf: PrT  sg/l: operations, sg: substitution node  sg/l: fuzzy object  sg/l: fuzzy object  page     Pages 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        1   1  0                             0.06  0.13  0.00  0.00   
72  (Christensen/Hansen 1993)  1993  ECPN (Extended CPN)  CPN  rf: CPN, sg/l: capacity colour set  rf: CPN  rf: CPN, sg: test, inhibitor  rf: CPN      X   Inhibition 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)  X        1  1     1     1                     0.13  0.27  0.00  0.00   
73  (David/Alla 1993)  1993  Timed Continuous Petri Nets   rf: P/T  sg/l: firing speed  rf: P/T  sg: real number        Continous 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.   X  X         1             1      1            0.10  0.07  0.33  0.00   
74  (Fehling 1993)  1993  Hierarchical Petri Nets  C/E  rf: C/E  rf: C/E  rf: C/E  rf: C/E    root (graphs)   Nodes are connected to nodes or to the root.    ... facilitate the modeling of large realworld systems, rather than using them for theoretical considerations (p. 148).    X      1  1                               0.06  0.13  0.00  0.00   
75  (Souissi 1993)  1993  DSSP (Deterministic Systems of sequential processes)  P/T  rf: P/T, sg: buffer  rf: P/T  rf: P/T  rf: P/T      X  (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).   X          1        1                      0.06  0.13  0.00  0.00   
76  (Trivedi/Kulkarni 1993)  1993  FSPN (Fluid Stochastic Petri Nets)   sg/l: discrete, continuous  sg: timed (exponentially distributed), immediate  sg/l: discrete, fluid  sg: fluid      X  No arcs are allowed between continuous places and immediate transitions.   ... to handle stochastic fluid flow systems (p. 24).  d     stochastic fluid systems       1             1     1             0.10  0.07  0.33  0.00   
77  (van der Aalst 1993)  1993  ITCPN (Interval Timed Coloured Petri Net)  CPN  sg: CPN  rf: CPN  rf: CPN  rf: CPN (timestamp)      X   The 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 realtime systems (p. 453).     X       1  m                1  1             0.13  0.13  0.33  0.00   
78  (Buchholz 1994)  1994  HHPN (Hierarchical High Level Petri Nets)  CPnets (= HPN)  rf: CPN  rf: CPN  rf: CPN  rf: CPN  aggregated view     Aggregated views receive input from transitions and produce output to places.    Apart from specification convenience HHPNs can be analysed very efficiently ... (p. 119).   X  X      1  1  1  1        1                      0.16  0.33  0.00  0.00   
79  (Christensen/Hansen 1994)  1994  CCPN  CPnets  rf: CPN  rf: CPN, sg/l: communication  rf: CPN  rf: CPN    channel (CSP, programming language)   Channels connect communication transitions.    ... include constructs making it easy to model synchronisation and synchronous communication (p. 160).  synchronization          1  1            1                  0.10  0.20  0.00  0.00   
80  (Diaz/Sénac 1994)  1994  TSPN (Time Stream Petri Nets)  Timed Petri nets  rf: P/T  sg/f: typing (firing: strong, weak, and, or, master)  sg/f: temporal validity interval       X    This 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, time     multimedia       1            0      1             0.06  0.07  0.17  0.00   
81  (Donatelli 1994)  1994  SGSPN (Superposed Generalized Stochastic Petri Nets)  GSPN  rf: GSPN  rf: GSPN, sg/l: synchronized  rf: GSPN  rf: GSPN      X   A GSPN is a set of GSPN that synchronize on a common subset of transitions of equal rate.  ... the major drawback 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).   X          1     1       1  1      1             0.16  0.27  0.17  0.00   
82  (Lakos/Christensen 1994)  1994   ECPN  rf: ECPN  rf: ECPN  rf: ECPN, sg/l: projected  rf: ECPN      X    It is general because ... it encompasses the other proposals for arc extensions ... (p. 338).     X       1  1    1  1     1                     0.16  0.33  0.00  0.00   
83  (Pedrycz/Peters 1999)  1994  GFPN (Generalized Fuzzy Petri Nets)  CPN  rf: CPN  rf: CPN  rf: CPN, sg/f: strenght of connection, reference points  rf: CPN      X    ... 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)  uncertainty     knowledge based reaoning      1  1                             0.06  0.13  0.00  0.00  Z  
84  (SibertinBlanc 1994)  1994  Cooperative Nets  HighLevel  sg: accept, return, sg/f: type  sg/l: function, action, sg: request, retrieve  sg/l: tuples of variables  sg: tuple of constants or object names of types      X    ... 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          1  1  1       1                      0.13  0.27  0.00  0.00   
85  (Barkaoui et al. 1995)  1995  Extended Non SelfControlling Nets  P/T, Extended FreeChoiceNets, Non Non SelfControlling Nets  rf: P/T  rf: P/T  rf: P/T  rf: P/T      X  (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 conflictfree path leading from a to b.   ... a new class of P/T nets for which the deadlocktrap property is a sufficient liveness condition (p. 25).   X       na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
86  (Best et al. 1995)  1995  Mnets (multilabeled)  Pr/T  rf: Pr/T, sg/l: status (entry, exit, internal)  rf: Pr/T, sg/l: communication interface  rf: Pr/T  rf: Pr/T      X  (1) There is always at least one entry and one exit place.   ... allow the modular construction of large highlevel nets from smaller components (p. 102).    X     [Benzaken et al. 1998]  1  1  1  1            1                  0.16  0.33  0.00  0.00   
87  (Haddad/Poitrenaud 1999)  1995  RPN (Recursive Petri nets)  P/T  rf: P/T  sg: elementary, abstract, final  rf: P/T  rf: P/T      X    The model of recursive Petri nets (RPNs) has been introduced in the field of multiagents systems in order to model flexible plans for agents (p. 228).      multiagent systems     i   1  i   i  i                         0.16  0.33  0.00  0.00  RC  A 
88  (Lakos 1995)  1995  Object Petri Nets  MCPN, CCPN  rf: MCPN, super, port  rf: MCPN, super  rf: MCPN, sg: inhibitor, test  rf: MCPN      X  (1) each transition has at most one input/output arc, (2) at most one inhibitor/test arc for each placetransition pair   ... by proposing a complete integration of objectoriented concepts ... into the Petri net formalism (p. 278).      object orientation    1  1  1      1    1  1    m                  0.23  0.47  0.00  0.00   
89  (Schöf et al. 1995)  1995  THORnets (Timed Hierarchical ObjectRelated)  Highlevel  sg: structured (multiset, stack, queue), sg/f: capacity  sg/l: activation condition, action block, delay, firing time, firing capacity, refined  sg: enabling, inhibitor, consuming, sg/l: weighted  sg: objects (OO programming)      X    The aim is ... to develop and implement an efficient modeling technique and methods for a fast sequential and distributed simulation of realtime systems ... (p. 412).   X        1  1  1  0   1  1     1         1  1            0.26  0.40  0.33  0.00  S, SC  
90  (Sénac et al. 1995)  1995  HTSPN (Hierarchical Time Stream Petri Nets)  TSPN (Time Stream Petri Nets)  sd/f: type (atomic = monomedia, composite = multimedia scenario, link type = hypermedia)  rf: TSPN  rf: TSPN  rf: TSPN      X    ... for the specification of temporal constraints and description of logical behaviour in distributed hypermedia systems (p. 451).  d     hypermedia    1    1            0      1      1  1       0.16  0.13  0.17  0.20  M  
91  (Colom 2003)  1995   P/T  sd/l: process, idle, resource, capacity  rf: P/T  rf: P/T  rf: P/T      X  selfloop free   The formulation of this applicationdriven problem [Flexible Manufacturing Systems, the author] in terms of Petri nets leads to a class of models... (p. 23).      manufacturing   (Ezpeleta et al. 1995)     1                    1     1      0.10  0.07  0.00  0.20   
92  (Horton 1998)  1996  FSPN (Fluid Stochastic Petri Nets)  GSPN  rf: GSPN, sg: fluid  rf: GSPN  rf: GSPN, sg: fluid, sg/f: rate  rf: GSPN, sg: fluid      X  Fluid flows connect only fluid places and timed transitions.   ... [FSPSN]... eine Möglichkeit zur Modellierung diskretkontinuierlicher Systeme bereitstellen...(S. 17) ... fassen bereits bekannte Zusatztechniken in einem Formalismus zusammen (S. 17).  d    X  discretecontinuous systems       1    1  1       1   1     1             0.19  0.27  0.33  0.00   
93  (Kindler/Walter 1996)  1996  Arctyped nets  highlevel nets  rf: PrT  sg/f: label  sg/l: multiset of terms, sg: arc types  sg: elements from the set of all multisets over an algebra      X    . ... provide an adequate level of abstraction for these kinds of applications [communication protocols, the author] (p. 289).  structure     protocols   [Kindler 2002]    1  1                             0.06  0.13  0.00  0.00   
94  (Murata et al. 1999)  1996  FTHN (FuzzyTiming High Level PN)  CPN  rf: CPN  rf: CPN  rf: CPN, sg/l: fuzzy delay  rf: 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).  time          1  m                1  1             0.13  0.13  0.33  0.00   
95  (Recalde et al. 1996)  1996  {SC}*ECS  P/T  rf: P/T, sg: buffer  rf: P/T  rf: P/T  rf: P/T      X  (1) if transitions share a preset, it is identical (equal conflict), (2) restrictions on buffers  Maybe, 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).   X       na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
96  (Bruni/Montanari 2000)  1997  Zerosafe nets  P/T  rf: P/T, sg: zeroplaces  rf: P/T  rf: P/T  rf: P/T      X    zerosafe nets, which extend PT nets with a simple mechanism for transition synchronization (p. 83).  synchronization           1            1                  0.06  0.13  0.00  0.00   
97  (Kindler 1997)  1997   P/T  rf: P/T, sg: input, output  sg: qiescent, progress  rf: P/T  rf: P/T      X    ... provides a semantical foundation for a modular verification method (p. 236).   X          1        1          i             0.10  0.13  0.17  0.00  PG  
98  (Kishinevsky et al. 1997)  1997  PCN (Place Chart Nets)  P/T  r: place chart  sg: preemptive  sg: preempting  rf: P/T      X   Preempting arcs remove all tokens, preemtive place charts abort the search.  The original Petri net model, unfortunately, lacks a notion of hierarchy (p. 329).  structure        1    1    i  i                         0.13  0.27  0.00  0.00   A 
99  (van der Aalst 1997)  1997  WFnets (WorkFlow nets)  P/T  rf: P/T, sg: source, sink  rf: P/T  rf: P/T  rf: P/T      X  The preset of source places and the postset of sink places are empty. (2) Every WFnet has one input place and one output place.   ... representation, validation and verification of workflow procedures (p. 407).  d  X    workflow       1       1                       0.06  0.13  0.00  0.00   
100  (Franceschinis/Ribaudo 1998)  1998  SWN (Stochastic Wellformed Net)  GSPN, CPN  rf: CPN  sg: timed (exponential distribution function), immediate, sg/f: weight, sg/l: guard  sg: inhibitor, sg/l: weighted sum of guarded tuples  rf: CPN      X    ... (SWNs), a high level SPN formalism in which behavioral symmetries can be automatically discovered and exploited (p. 387) ...   X         1  m     1       1       1             0.16  0.27  0.17  0.00   
101  (Kindler/Völzer 1998)  1998  Algebraic system net   sg: sorted  sg/l: guard  sg: flexible  sg: SIGterms of some sort      X    ... lack a feature for modeling distributed network algortihms, viz. flexible arcs (p. 345). .. are better suited for modeling distributed algorithms (p. 345).  d     algorithms      1  1    1                          0.10  0.20  0.00  0.00   
102  (Bastide et al. 1999)  1999  CO (Coperative Objects)  CPN  sg/l: token type  sg/l: precondition, action  sg/l: tuples of variables, multiplicity), sg: test, inhibitor  sg: tuples of typed values      X    ... aims at providing a suitable solution to the problem of behavioural specification of distributed objects, in the context of CORBA (p. 67).  d     object orientation      1  1  1    1     1                     0.16  0.33  0.00  0.00   
103  (Fanchon 1999)  1999  Trace Channel nets  CPN, FIFO  r: channel  rf: CPN  sg/l: traces  sg: traces      X    Trace Channel Nets can be comprehensively seen as a 'natural' generalization of existing classes of nets (p. 305).     X     na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
104  (Recalde et al. 1996)  1999  Autonomous Continuous P/T Systems  P/T  rf: P/T  rf: P/T  rf: P/T  sg: fluid      X    Discrete 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).   X          1             1                 0.06  0.07  0.17  0.00   
105  (Schneider/Wehler 1999)  1999  Artin nets  CPN  rf: CPN  rf: CPN  rf: CPN  rf: CPN      X  restrictions on the colour sets of places and transitions   We introduce Artin nets a subclass of coloured nets, which can be handled by methods from commutative Algebra (p. 248).   X       na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na  na 
106  (Ballarini et al. 2000)  2000  Parametric Stochastic WellFormed Nets  Stochastic WellFormed Nets  sg: coloured (cartesian product of basic color classes)  sg: coloured, guards, priority, labeled (import/export functions)  sg: labeled (variables typed by colour, arithmetic expressions), inhibitor  sg: elements from a basic or parametric colour class      X    ... in order to increase modularity and reuse of the modelling efforts (p. 43).       X          1                         0.03  0.07  0.00  0.00   
107  (Vogler 2000)  2000  Petri Nets with Time Bounds and Interface  P/T  rf: P/T, sg: input, output  sg/f: time bounds {0, 1}  X  X      X    unknown                  1        1          1  1            0.13  0.13  0.33  0.00   
108  (Deussen 2001)  2001  RN (Register Net)  EN  rf: EN  sg/l: predicates, sg/f: register treatment  rf: EN, reading  sg: value from a register  register     Register 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).  d  X    hardware      1  1         1                 1     0.13  0.20  0.00  0.10   
109  (Köhler et al. 2001)  2001  Reference Nets  CPN  rf: CPN   rf: CPN, sg: reservation, test, inhibitor  sg: object net  synchronous channels     Channels connect one transition to exactly one other for one occurrence.   Reservation arcs reserve tokens for a transition.  unknown            (Köhler 2004)    1      1        1                  0.10  0.20  0.00  0.00   
110  (Nielsen et al. 2001)  2001  Distributed TimedArc Petri Nets  (Zeitbehaftetes Netz)  (sg: capacity)  rf: P/T  sg/f: time intervals  sg/l: age  synchronization relation     The synchronization relation is defined on at least two places.    ... allowing a local timing as well as distributed time synchronization (p. 23).  time, synchronization          1  m            0     1              0.10  0.13  0.17  0.00   
111  (Di Marzo Serugendo et al. 2002)  2002  RealTime Synchronized Petrinets   sg/f: capacity  sg: methods, sg/l: time interval  sg: inhibitor  sg: time stamped  synchronization expression     Methods and Transitions may request synchronization with methods.    Our proposal enables one to define complex systems with compact specifications ... (p. 142)    X         1     1        1     1              0.13  0.20  0.17  0.00   
112  (Stork/van Glabbeek 2002)  2002   PrT  rf: PrT, sg: refinement (guarded), input, output  rf: PrT  rf: PrT  sg: structured      X    .... Petri net theory as is stands is incapable of expressing properties we seek in such extended workflows (p. 395).  d     workflow    1   1  m        1                      0.13  0.27  0.00  0.00  R  
113  (Fleischhack/Pelz 2003)  2003  Hierarchical Duration Mnets  Timed Mnets, CPN  sg: labeled (type, status)  sg/l: communication (labeled by guard, action, range for duration), hierarchical (labeled by hierarchical actions)  rf: CPN  rf: CPN      Refined 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, time        0  1  1                  a  1            0.13  0.13  0.33  0.00   
114  (Genc/Lafortune 2003)  2003   (P/T?)  rf: P/T  sg/l: observable/unobservable fault events  sg/l: weight  sg: {0, 1}, types      X    .... where some of the transitions are labeled by different fault events (p. 317).  d  (X)    fault tolerant systems      1  1                             0.06  0.13  0.00  0.00   
115  (Matsuno et al. 2003)  2003  HFBN (Hybrid functional Petri net)  Hybrid PN  sg: discrete, continuous  sg: discrete, continuous, sg/l: function  sg/l: weight, inhibitory, test, function  sg: integer, real values      X   Funtional continuous transitions control the speed/condition of consumption/production/firing.  ... an extension ... which allows us to model biopathways naturally and efficiently (p. 3).  d     biology       1     1     1     1                 0.13  0.20  0.17  0.00   