Skip to main content
SpringerLink
Log in

The Complexity of Synthesis for 43 Boolean Petri Net Types

  • Conference paper
  • First Online:
Book cover Theory and Applications of Models of Computation (TAMC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11436))

Abstract

Synthesis for a type of Petri nets is the problem of finding, for a given transition system A, a Petri net N of this type having a state graph that is isomorphic to A, if such a net exists. This paper studies the computational complexity of synthesis for 43 boolean types of Petri nets. It turns out that for 36 of these types synthesis can be done in polynomial time while for the other seven it is NP-hard.

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

Access this chapter

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

Institutional subscriptions

References

  1. van der Aalst, W.M.P.: Process Mining - Discovery, Conformance and Enhancement of Business Processes. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19345-3

    Book  MATH  Google Scholar 

  2. 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 

  3. 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 

  4. Badouel, E., Bernardinello, L., Darondeau, P.: Petri Net Synthesis. Texts in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47967-4

    Book  MATH  Google Scholar 

  5. Badouel, É., Caillaud, B., Darondeau, P.: Distributing finite automata through Petri net synthesis. Formal Asp. Comput. 13(6), 447–470 (2002). https://doi.org/10.1007/s001650200022

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Cortadella, J., Kishinevsky, M., Kondratyev, A., Lavagno, L., Yakovlev, A.: A region-based theory for state assignment in speed-independent circuits. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 16(8), 793–812 (1997). https://doi.org/10.1109/43.644602

    Article  MATH  Google Scholar 

  8. Ehrenfeucht, A., Rozenberg, G.: Partial (set) 2-structures. Part I: basic notions and the representation problem. Acta Informatica 27(4), 315–342 (1990). https://doi.org/10.1007/BF00264611

    Article  MathSciNet  MATH  Google Scholar 

  9. Goldmann, M., Russell, A.: The complexity of solving equations over finite groups. Inf. Comput. 178(1), 253–262 (2002). https://doi.org/10.1006/inco.2002.3173

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. 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 

  13. 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 

  14. 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 

  15. Tarjan, R.E.: Finding optimum branchings. Networks 7(1), 25–35 (1977). https://doi.org/10.1002/net.3230070103

    Article  MathSciNet  MATH  Google Scholar 

  16. Thiagarajan, P.S.: Elementary net systems. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) Petri Nets: Central Models and Their Properties. LNCS, vol. 254, pp. 26–59. Springer, Heidelberg (1986). https://doi.org/10.1007/BFb0046835

    Chapter  Google Scholar 

  17. Tredup, R., Rosenke, C.: Narrowing down the hardness barrier of synthesizing elementary net systems. In: Schewe, S., Zhang, L. (eds.) 29th International Conference on Concurrency Theory, CONCUR 2018. LIPIcs, Beijing, China, 4–7 September 2018, vol. 118, pp. 16:1–16:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018). https://doi.org/10.4230/LIPIcs.CONCUR.2018.16

  18. Tredup, R., Rosenke, C.: Towards completely characterizing the complexity of Boolean nets synthesis. CoRR abs/1806.03703 (2018). http://arxiv.org/abs/1806.03703

  19. 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 

Download references

Author information

Authors and Affiliations

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

    Ronny Tredup & Christian Rosenke

Authors
  1. Ronny Tredup
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Rosenke
    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. Anna University, Chennai, India

    T.V. Gopal

  2. Waseda University, Kitakyushu, Japan

    Junzo Watada

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tredup, R., Rosenke, C. (2019). The Complexity of Synthesis for 43 Boolean Petri Net Types. In: Gopal, T., Watada, J. (eds) Theory and Applications of Models of Computation. TAMC 2019. Lecture Notes in Computer Science(), vol 11436. Springer, Cham. https://doi.org/10.1007/978-3-030-14812-6_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-14812-6_38

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14811-9

  • Online ISBN: 978-3-030-14812-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation