Reachability in live and safe free-choice Petri nets is NP-complete

We study the complexity of several standard problems for 1-safe Petri nets and some of its subclasses. We prove that reachability, liveness, and deadlock are all PSPACE-complete for 1-safe nets. We also prove that deadlock is NP-complete for free-choice nets and for 1-safe free-choice nets. Finally, we prove that for arbitrary Petri nets, deadlock is equivalent to reachability and liveness. This paper is to be presented at FST & TCS, Foundations of Software Technology & Theoretical Computer Science, to be held 15-17 December 1993, in Bombay, India.A version of the paper with most proofs omitted is to appear in the proceedings.

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Combining free choice and time in Petri nets

Journal of Logical and Algebraic Methods in Programming ◽

10.1016/j.jlamp.2018.11.006 ◽

2020 ◽

Vol 110 ◽

pp. 100426

Author(s):

S. Akshay ◽

Loïc Hélouët ◽

Ramchandra Phawade

Keyword(s):

Petri Nets ◽

Free Choice

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Free-choice Petri nets-an algebraic approach

IEEE Transactions on Automatic Control ◽

10.1109/9.545714 ◽

1996 ◽

Vol 41 (12) ◽

pp. 1751-1778 ◽

Cited By ~ 28

Author(s):

F. Baccelli ◽

S. Foss ◽

B. Gaujal

Keyword(s):

Petri Nets ◽

Free Choice ◽

Algebraic Approach

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Target-oriented Petri Net Synthesis

A Mosaic of Computational Topics: from Classical to Novel ◽

10.3233/stal200007 ◽

2020 ◽

Author(s):

Eike Best ◽

Raymond Devillers ◽

Evgeny Erofeev ◽

Harro Wimmel

Keyword(s):

Petri Nets ◽

Petri Net ◽

Transition System ◽

Efficient Synthesis ◽

Transition Systems ◽

Np Complete ◽

Full Class ◽

Petri Net Synthesis ◽

Labelled Transition System ◽

Additional Constraints

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

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