Proving Non-Reachabililty by Modulo-Place-Invariants

The reachability problem of Petri nets is the problem of deciding whether a marking can be reached from the initial marking by a sequence of occurrences of transitions. It is decidable in general, but it has a very high complexity.

[1]  D. Garling,et al.  Algebra, Volume 1 , 1969, Mathematical Gazette.

[2]  Richard J. Lipton,et al.  Exponential space complete problems for Petri nets and commutative semigroups (Preliminary Report) , 1976, STOC '76.

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  M. Garey.  Johnson: computers and intractability: a guide to the theory of np- completeness (freeman , 1979 .

[5]  Ravi Kannan,et al.  Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix , 1979, SIAM J. Comput..

[6]  Kurt Jensen.  High-Level Petri Nets , 1982, European Workshop on Applications and Theory of Petri Nets.

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

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

[9]  Wolfgang Reisig,et al.  Petri Nets , 1985, EATCS Monographs on Theoretical Computer Science.

[10]  Matthias Jantzen.  Complexity of Place/Transition Nets , 1986, Advances in Petri Nets.

[11]  Michael Pohst,et al.  Algorithmic algebraic number theory , 1989, Encyclopedia of mathematics and its applications.

[12]  H. Zassenhaus,et al.  Algorithmic algebraic number theory: Preface , 1989 .

[13]  Grzegorz Rozenberg,et al.  High-level Petri Nets: Theory And Application , 1991 .

[14]  Jörg Desel,et al.  Reachability in Cyclic Extended Free-Choice Systems , 1993, Theor. Comput. Sci..