Skip to main content
SpringerLink
Log in
Book cover

International Colloquium on Theoretical Aspects of Computing

ICTAC 2020: Theoretical Aspects of Computing – ICTAC 2020 pp 123–142Cite as

The Complexity of Boolean State Separation

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12545))

Abstract

For a Boolean type of nets \(\tau \), a transition system A is synthesizeable into a \(\tau \)-net N if and only if distinct states of A correspond to distinct markings of N, and N prevents a transition firing if there is no related transition in A. The former property is called \(\tau \)-state separation property (\(\tau \)-SSP) while the latter – \(\tau \)-event/state separation property (\(\tau \)-ESSP). A is embeddable into the reachability graph of a \(\tau \)-net N if and only if A has the \(\tau \)-SSP. This paper presents a complete characterization of the computational complexity of \(\tau \) -SSP for all Boolean Petri net types.

E. Erofeev—Supported by DFG through grant Be 1267/16-1 ASYST.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Badouel, E., Bernardinello, L., Darondeau, P.: Polynomial algorithms for the synthesis of bounded nets. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds.) CAAP 1995. LNCS, vol. 915, pp. 364–378. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-59293-8_207

    Chapter  Google Scholar 

  2. Badouel, E., Bernardinello, L., Darondeau, P.: The synthesis problem for elementary net systems is NP-complete. Theor. Comput. Sci. 186(1–2), 107–134 (1997). https://doi.org/10.1016/S0304-3975(96)00219-8

    Article  MathSciNet  MATH  Google Scholar 

  3. Badouel, E., Bernardinello, L., Darondeau, P.: Petri Net Synthesis. TTCSAES. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47967-4

    Book  MATH  Google Scholar 

  4. Badouel, E., Darondeau, P.: Trace nets and process automata. Acta Inf. 32(7), 647–679 (1995). https://doi.org/10.1007/BF01186645

    Article  MathSciNet  MATH  Google Scholar 

  5. Best, E., Devillers, R.R.: Pre-synthesis of Petri nets based on prime cycles and distance paths. Sci. Comput. Program. 157, 41–55 (2018). https://doi.org/10.1016/j.scico.2017.07.005

    Article  Google Scholar 

  6. Chatain, T., Haar, S., Kolcák, J., Paulevé, L., Thakkar, A.: Concurrency in Boolean networks. Nat. Comput. 19(1), 91–109 (2020). https://doi.org/10.1007/s11047-019-09748-4

    Article  MathSciNet  Google Scholar 

  7. Esparza, J., Nielsen, M.: Decidability issues for Petri nets - a survey. Bull. EATCS 52, 244–262 (1994)

    MATH  Google Scholar 

  8. Kleijn, J., Koutny, M., Pietkiewicz-Koutny, M., Rozenberg, G.: Step semantics of Boolean nets. Acta Inf. 50(1), 15–39 (2013). https://doi.org/10.1007/s00236-012-0170-2

    Article  MathSciNet  MATH  Google Scholar 

  9. Montanari, U., Rossi, F.: Contextual occurrence nets and concurrent constraint programming. In: Schneider, H.J., Ehrig, H. (eds.) Graph Transformations in Computer Science. LNCS, vol. 776, pp. 280–295. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-57787-4_18

    Chapter  Google Scholar 

  10. Montanari, U., Rossi, F.: Contextual nets. Acta Inf. 32(6), 545–596 (1995). https://doi.org/10.1007/BF01178907

    Article  MathSciNet  MATH  Google Scholar 

  11. Moore, C., Robson, J.M.: Hard tiling problems with simple tiles. Discret. Comput. Geom. 26(4), 573–590 (2001). https://doi.org/10.1007/s00454-001-0047-6

    Article  MathSciNet  MATH  Google Scholar 

  12. Pietkiewicz-Koutny, M.: transition systems of elementary net systems with inhibitor arcs. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 310–327. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-63139-9_43

    Chapter  Google Scholar 

  13. Rozenberg, G., Engelfriet, J.: Elementary net systems. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 12–121. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-65306-6_14

    Chapter  Google Scholar 

  14. Schlachter, U.: Over-approximative Petri net synthesis for restricted subclasses of nets. In: Klein, S.T., Martín-Vide, C., Shapira, D. (eds.) LATA 2018. LNCS, vol. 10792, pp. 296–307. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77313-1_23

    Chapter  Google Scholar 

  15. Schlachter, U., Wimmel, H.: Optimal label splitting for embedding an LTS into an arbitrary Petri net reachability graph is NP-complete. CoRR abs/2002.04841 (2020). https://arxiv.org/abs/2002.04841

  16. Schmitt, V.: Flip-flop nets. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 515–528. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-60922-9_42

    Chapter  Google Scholar 

  17. Tredup, R.: The complexity of synthesizing nop-equipped Boolean nets from g-bounded inputs (technical report) (2019)

    Google Scholar 

  18. Tredup, R.: Fixed parameter tractability and polynomial time results for the synthesis of b-bounded Petri nets. In: Donatelli, S., Haar, S. (eds.) PETRI NETS 2019. LNCS, vol. 11522, pp. 148–168. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21571-2_10

    Chapter  Google Scholar 

  19. Tredup, R.: Hardness results for the synthesis of b-bounded Petri nets. In: Donatelli, S., Haar, S. (eds.) PETRI NETS 2019. LNCS, vol. 11522, pp. 127–147. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21571-2_9

    Chapter  Google Scholar 

  20. Tredup, R.: Parameterized complexity of synthesizing b-bounded (m, n)-T-systems. In: Chatzigeorgiou, A., et al. (eds.) SOFSEM 2020. LNCS, vol. 12011, pp. 223–235. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-38919-2_19

    Chapter  MATH  Google Scholar 

  21. Tredup, R., Erofeev, E.: The complexity of Boolean state separation (technical report) (2020). submitted to arxive.org

    Google Scholar 

  22. Tredup, R., Erofeev, E.: On the complexity of synthesis of nop-free Boolean Petri nets. In: van der Aalst, W.M.P., Bergenthum, R., Carmona, J. (eds.) Proceedings of the International Workshop on Algorithms & Theories for the Analysis of Event Data 2020 Satellite event of the 41st International Conference on Application and Theory of Petri Nets and Concurrency Petri Nets 2020, Virtual Workshop, June 24, 2020. CEUR Workshop Proceedings, vol. 2625, pp. 66–84. CEUR-WS.org (2020). http://ceur-ws.org/Vol-2625/paper-05.pdf

  23. Tredup, R., Rosenke, C.: The complexity of synthesis for 43 boolean petri net types. In: Gopal, T.V., Watada, J. (eds.) TAMC 2019. LNCS, vol. 11436, pp. 615–634. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14812-6_38

  24. Tredup, R., Rosenke, C., Wolf, K.: Elementary net synthesis remains NP-complete even for extremely simple inputs. In: Khomenko, V., Roux, O.H. (eds.) PETRI NETS 2018. LNCS, vol. 10877, pp. 40–59. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91268-4_3

    Chapter  Google Scholar 

  25. Vogler, W., Semenov, A., Yakovlev, A.: Unfolding and finite prefix for nets with read arcs. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 501–516. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055644

    Chapter  Google Scholar 

  26. Wimmel, H.: Presynthesis of bounded choice-free or fork-attribution nets. Inf. Comput. 271, 104482 (2020)

    Article  MathSciNet  Google Scholar 

  27. Yakovlev, A., Koelmans, A., Semenov, A.L., Kinniment, D.J.: Modelling, analysis and synthesis of asynchronous control circuits using Petri nets. Integration 21(3), 143–170 (1996). https://doi.org/10.1016/S0167-9260(96)00010-7

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Theoretische Informatik, Universität Rostock, Albert-Einstein-Straße 22, 18059, Rostock, Germany

    Ronny Tredup

  2. Department of Computing Science, Carl von Ossietzky Universität Oldenburg, 26111, Oldenburg, Germany

    Evgeny Erofeev

Authors
  1. Ronny Tredup
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Evgeny Erofeev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ronny Tredup .

Editor information

Editors and Affiliations

  1. Western Norway University of Applied Sciences, Bergen, Norway

    Violet Ka I Pun

  2. Western Norway University of Applied Sciences, Bergen, Norway

    Volker Stolz

  3. Federal University of Sao Carlos, Sao Carlos, Brazil

    Adenilso Simao

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tredup, R., Erofeev, E. (2020). The Complexity of Boolean State Separation. In: Pun, V.K.I., Stolz, V., Simao, A. (eds) Theoretical Aspects of Computing – ICTAC 2020. ICTAC 2020. Lecture Notes in Computer Science(), vol 12545. Springer, Cham. https://doi.org/10.1007/978-3-030-64276-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-64276-1_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-64275-4

  • Online ISBN: 978-3-030-64276-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation