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Complexity Results for 1-safe Nets

Allan Cheng, Javier Esparza, Jens Palsberg
1993 DAIMI Report Series  
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.  ...  <p>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.  ...  Thiagarajan, and the anonymous referees for helpful comments on a draft of the paper.  ... 
doi:10.7146/dpb.v22i455.6773 fatcat:kxvraxqzmbd67ps5uuch7bfsqy

Complexity results for 1-safe nets [chapter]

Allan Cheng, Javier Esparza, Jens Palsberg
1993 Lecture Notes in Computer Science  
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.  ...  Thiagarajan, and the anonymous referees for helpful comments on a draft of the paper.  ... 
doi:10.1007/3-540-57529-4_66 fatcat:2zbpiqzsifcuncr467vjpt7agi

On the Decidability and Complexity of Diagnosability for Labeled Petri Nets

Xiang Yin, Stephane Lafortune
2017 IEEE Transactions on Automatic Control  
To the best of our knowledge, this is the first paper that establishes decidability and complexity results for diagnosability of unbounded Petri nets.  ...  Then, we show that checking diagnosability for unbounded Petri nets is EXPSPACE-complete. This complexity result is further extended to various sub-classes of Petri nets.  ...  In particular, they sincerely thank an anonymous reviewer who pointed out a mistake in an earlier version of Theorem IV.1.  ... 
doi:10.1109/tac.2017.2699278 fatcat:3li6wbjt4zbz7io4byfliudmoy

Synthesis and Analysis of Product-Form Petri Nets [chapter]

S. Haddad, J. Mairesse, H-T. Nguyen
2011 Lecture Notes in Computer Science  
Here we address three relevant issues for product-form Petri nets which were left fully or partially open: (1) we provide a sound and complete set of rules for the synthesis; (2) we characterise the exact  ...  Being first introduced in queueing networks, it has been adapted to Markovian Petri nets.  ...  We would like to thank the anonymous referess whose numerous and pertinent suggestions have been helpful in preparing the final version of the paper.  ... 
doi:10.1007/978-3-642-21834-7_16 fatcat:vwso3nxkbbch7n7yya5mxujpwi

On the Complexity of Bisimulation Problems for Basic Parallel Processes [chapter]

Richard Mayr
2000 Lecture Notes in Computer Science  
We show that strong bisimilarity of BPP is co-N P-hard. Weak bisimilarity of BPP is not known to be decidable, but an NP lower bound has been shown in [31] .  ...  Finally, we show that the problems if a BPP is regular (i.e., finite) w.r.t. strong and weak bisimilarity are co-N P-hard and p 2 -hard, respectively.  ...  Finally, both strong bisimilarity of Petri nets and finite automata and finiteness of Petri nets w.r.t. strong bisimilarity are EXPSPACE-hard.  ... 
doi:10.1007/3-540-45022-x_29 fatcat:tnd2riqm35f4bcio42aobhayke

Complexity results for 1-safe nets

Allan Cheng, Javier Esparza, Jens Palsberg
1995 Theoretical Computer Science  
Finally, we prove that for arbitrary Petri nets, deadlock is equivalent to reachability and liveness. .  ...  We study the complexity of several standard problems for l-safe Petri nets and some of its subclasses. We prove that reachability, liveness, and deadlock are all PSPACE-complete for l-safe nets.  ...  Thiagarajan, and the anonymous referees for helpful comments on a draft of the paper.  ... 
doi:10.1016/0304-3975(94)00231-7 fatcat:tgp7u5pvhze4fbyupzvbj72yau

The Logical View on Continuous Petri Nets

Michael Blondin, Alain Finkel, Christoph Haase, Serge Haddad
2017 ACM Transactions on Computational Logic  
We are grateful to the anonymous reviewers of TACAS'16 and ACM TOCL for their comments and suggestions.  ...  ACKNOWLEDGMENTS We would like to thank Vincent Antaki for an early implementation of the polynomial-time algorithm of Fraca and Haddad [2015] , and also Gilles Geeraerts for his support with the MIST  ...  To the best of our knowledge, the following is the first decidability and complexity result for (structural) ε-liveness. PROPOSITION 4.8. ε-Liveness and structural ε-liveness are decidable in Σ P 3 .  ... 
doi:10.1145/3105908 fatcat:a7crufoegzexzhndl6j2aviknm

Co-finiteness and Co-emptiness of Reachability Sets in Vector Addition Systems with States [chapter]

Petr Jančar, Jérôme Leroux, Grégoire Sutre
2018 Lecture Notes in Computer Science  
The studied problems have been motivated by a recent result for structural liveness of Petri nets; this problem has been shown decidable by Jančar in 2017 but its complexity has not been clarified.  ...  The coverability and boundedness problems are well-known exponential-space complete problems for vector addition systems with states (or Petri nets).  ...  As the most relevant for us we recall the reachability and liveness problems for Petri nets.  ... 
doi:10.1007/978-3-319-91268-4_10 fatcat:ik4dfe2z5nesxkwpcydes4vgtq

Parameterized Analysis of Immediate Observation Petri Nets [article]

Javier Esparza, Mikhail Raskin, Chana Weil-Kennedy
2019 arXiv   pre-print
We study the parameterized reachability, coverability, and liveness problems for immediate observation Petri nets.  ...  We introduce immediate observation Petri nets, a class of interest in the study of population protocols (a model of distributed computation), and enzymatic chemical networks.  ...  We thank three anonymous reviewers for numerous suggestions to improve readability, and Pierre Ganty for many helpful discussions.  ... 
arXiv:1902.03025v2 fatcat:2fz55b5rzze4vgk5gtvmoaj7xe

Complexity of the Soundness Problem of Bounded Workflow Nets [chapter]

Guan Jun Liu, Jun Sun, Yang Liu, Jin Song Dong
2012 Lecture Notes in Computer Science  
Aalst et al. proved that the soundness problem is decidable, and proposed (but not proved) that the soundness problem is EXPSPACE-hard.  ...  Classical workflow nets (WF-nets) are an important class of Petri nets that are widely used to model and analyze workflow systems.  ...  Acknowledgement We would like to thank Professor W.M.P. van der Aalst who encourages us to explore the complexity of the soundness problem for general WF-nets, and also thank four anonymous reviewers whose  ... 
doi:10.1007/978-3-642-31131-4_6 fatcat:36gix3m2vbg4hjilneuysktfei

Decidability and complexity of Petri net problems — An introduction [chapter]

Javier Esparza
1998 Lecture Notes in Computer Science  
A collection of 10 "rules of thumb" is presented that helps to determine the decidability and complexity of a large number of Petri net problems.  ...  They suggested the correct programs of this version. Zdenek Sawa also found some more mistakes. The PSPACEalgorithm for CTL of Section 4 is joint work with Peter Rossmanith.  ...  Many thanks also to Serge Haddad and Zdenek Sawa found a mistake in the version of this paper which appeared in LNCS 1491: the programs AE ½´ µ and AE ¾´ µ given in Section 9 were incorrect.  ... 
doi:10.1007/3-540-65306-6_20 fatcat:fivpidigergwdjikofnaqutvzu

Algorithmic verification of asynchronous programs

Pierre Ganty, Rupak Majumdar
2012 ACM Transactions on Programming Languages and Systems  
We show that liveness verification for finite-data asynchronous programs is decidable and polynomial-time equivalent to Petri Net reachability.  ...  Our main technical construction is a polynomial-time semantics-preserving reduction from asynchronous programs to Petri Nets and conversely.  ...  The expspace-hardness follows from the corresponding hardness for Petri net reachability.  ... 
doi:10.1145/2160910.2160915 fatcat:k5upqup32vhrdnkqfj3rt4y6ta

A Subclass of Petri Net with Reachability Equivalent to State Equation Satisfiability: Live Single Branch Petri Net

Qian Gao, Young Im Cho
2013 International Journal of Fuzzy Logic and Intelligent Systems  
This paper proposes and proves three propositions in order to present a subclass of a Petri Net, the live single-branch Petri Net, whose reachability is equivalent to the satisfiability of the state equation  ...  Petri Nets are a system description and analysis tool. Reachability is one of the most basic properties in Petri Net research.  ...  In fact, this problem was shown to be EXPSPACE-hard [4] years before it was shown to be decidable at all. Papers continue to be published on how to decide the reachability efficiently [5] .  ... 
doi:10.5391/ijfis.2013.13.3.200 fatcat:fq3wcemzknb4ffbllmk2i2aram

Deciding structural liveness of Petri nets [article]

Petr Jancar
2016 arXiv   pre-print
Here we show that the structural liveness problem for Petri nets is decidable.  ...  Somewhat surprisingly, the decidability status of the problem if a net is structurally live, i.e. if there is an initial marking for which it is live, has remained open, as also a recent paper (Best and  ...  I would like to thank to Eike Best for drawing my attention to the problem of structural liveness studied in this paper.  ... 
arXiv:1608.02327v1 fatcat:4udowsuogbghvhi3m33bwizaca

Decidability Issues for Petri Nets

Javier Esparza, Mogens Nielsen
1994 BRICS Report Series  
This is a survey of some decidability results for Petri nets, covering the last three decades.  ...  The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics.  ...  Acknowledgements Thanks to David de Frutos, Matthias Jantzen, Jean-Luc Lambert and Elisabeth Pelz for providing useful information.  ... 
doi:10.7146/brics.v1i8.21662 fatcat:jyrntthfg5gh5mu77soacgwbsu
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