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Decidability Issues for Petri Nets - a survey (1994) [62 citations — 5 self]

by Javier Esparza ,  Mogens Nielsen
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Abstract:

: We survey 25 years of research on decidability issues for Petri nets. We collect results on the decidability of important properties, equivalence notions, and temporal logics. 1. Introduction Petri nets are one of the most popular formal models for the representation and analysis of parallel processes. They are due to C.A. Petri, who introduced them in his doctoral dissertation in 1962. Some years later, and independently from Petri's work, Karp and Miller introduced vector addition systems [47], a simple mathematical structure which they used to analyse the properties of "parallel program schemata', a model for parallel computation. In their seminal paper on parallel program schemata, Karp and Miller studied some decidability issues for vector addition systems, and the topic continued to be investigated by other researchers. When Petri's ideas reached the States around 1970, it was observed that Petri nets and vector addition systems were mathematically equivalent, even though thei...

Citations

2701 Communication and Concurrency – Milner - 1989
238 The linear time – branching time spectrum II (the semantics of sequential systems with silent moves – Glabbeek - 1993
179 Modal and Temporal Logics – Stirling - 1991
109 An algorithm for the general Petri net reachability problem – Mayr - 1984
102 Parallel program schemata – Karp, Miller - 1969
100 Model checking using net unfoldings – Esparza - 1993
93 and A.Pnueli. Marked Directed Graphs – Commoner, Holt, et al. - 1971
72 Decidability and Decomposition in Process Algebras – Christensen - 1993
61 Decidability of reachability in vector addition systems – Kosaraju - 1982
49 Bisimulation equivalence is decidable for basic parallel processes – Christensen, Hirshfeld, et al. - 1993
49 The reachability problem requires exponential space – Lipton - 1976
32 Complexity results for 1-safe nets – Cheng, Esperza - 1993
32 On the reachability problem for 5-dimensional vector addition systems, Theoret – Hopcroft, Pansiot - 1979
31 Decidability questions for Petri nets – Hack - 1976
29 Verifying Temporal Properties of Systems (Birkh"auser – Bradfield - 1991
29 Decidability of a temporal logic problem for petri nets – Jancar - 1990
23 Petri nets and the equivalence problem – Hirshfeld - 1994
23 Undecidable equivalence for basic parallel processes – Huttel - 1994
21 Some decision problems related to the reachability problem for Petri nets – Araki, Kasami - 1977
21 Commutative grammars: The complexity of uniform word problems – Huynh - 1983
21 The Covering and Boundedness Problems for Vector Addition Systems – Rackoff - 1978
19 Decidability questions for bisimilarity of Petri nets and some related problems – Jančar - 1994
18 The Residue of Vector Sets with Applications to Decidability Problems in Petri Nets – Valk, Jantzen - 1985
17 A Taxonomy of Fairness and Temporal Logic Problems for Petri Nets – Howell, Rosier, et al. - 1991
17 Computation: Finite and Infinite Machines. Prentice-Hall Series in Automatic Computation – Minsky - 1967
16 Linear algebra in net theory – Memmi, Roucairol - 1980
16 The Mathematics of Petri Nets – Reutenauer - 1990
15 Exponential space complete problems for Petri nets and commutative semigroups – Cardoza, Lipton, et al. - 1976
15 Problems concerning fairness and temporal logic for conflict-free Petri nets, Theoret – Howell, Rosier - 1989
15 The complexity of the finite containment problem for Petri nets – Mayr, Meyer - 1981
15 A unified approach for deciding the existence of certain Petri net paths – Yen - 1992
14 Petri Nets and Regular Languages – Valk, Vidal-Naquet - 1981
13 Properties of conflict-free and persistent Petri nets – Landweber, Robertson - 1978
13 Persistence of vector replacement systems is decidable – Mayr - 1981
12 Rabin's proof of the undecidability of the reachability set inclusion problem for vector addition systems – Baker - 1973
12 A polynomial-time algorithm to decide liveness of bounded free choice nets – Esparza, Silva - 1992
10 On the Decidability of Model Checking for Several -calculi and Petri Nets – Esparza - 1994
10 Some complexity bounds for problems concerning finite and 2-dimensional vector addition systems with states, Theoret – Howell, Rosier, et al. - 1986
10 Deciding true concurrency equivalences on finite safe nets – Jategaonkar, Meyer - 1993
9 Fairness and Conspiracies – Best - 1984
9 Normal and sinkless Petri nets – Howell, Rosier, et al. - 1989
9 A multiparameter analysis of the boundedness problem for vector addition systems – Rosier, Yen - 1986
9 A fresh look at free choice nets – Thiagarajan, Voss - 1984
8 A fundamental theorem of asynchronous parallel computation – Keller - 1975
8 A structure to decide reachability in Petri nets – Lambert - 1992
8 The Complexity of the Word Problems for Commutative – Mayr, Meyer - 1982
8 local model checking in the linear time mu-calculus – Stirling, Walker, et al. - 1990
7 Model Checking of Persistent Petri Nets – Best, Esparza - 1992
7 Reachability in cyclic extended free-choice systems – Desel, Esparza - 1993
7 Completeness results for conflict-free vector replacement systems – Howell, Rosier - 1988