: 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...
|
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
|
