Skip to main content
SpringerLink
Log in

Shallow Non-confluent P Systems

  • Conference paper
  • First Online:
Membrane Computing (CMC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10105))

Included in the following conference series:

Abstract

We prove that non-confluent (i.e., strongly nondeterministic) P systems with active membranes working in polynomial time are able to simulate polynomial-space nondeterministic Turing machines, and thus to solve all \({\mathbf{PSPACE }}\) problems. Unlike the confluent case, this result holds for shallow P systems. In particular, depth 1 (i.e., only one membrane nesting level and using elementary membrane division only) already suffices, and neither dissolution nor send-in communication rules are needed.

This work was partially supported by Fondo d’Ateneo (FA) 2015 of Università degli Studi di Milano-Bicocca: “Complessità computazionale e applicazioni crittografiche di modelli di calcolo bioispirati”.

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. Alhazov, A., Freund, R.: On the efficiency of P systems with active membranes and two polarizations. In: Mauri, G., Păun, G., Pérez-Jiménez, M.J., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 146–160. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31837-8_8

    Chapter  Google Scholar 

  2. Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Simulating elementary active membranes. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Sosík, P., Zandron, C. (eds.) CMC 2014. LNCS, vol. 8961, pp. 284–299. Springer, Heidelberg (2014). doi:10.1007/978-3-319-14370-5_18

    Google Scholar 

  3. Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Membrane division, oracles, and the counting hierarchy. Fundam. Informaticae 138(1–2), 97–111 (2015)

    MathSciNet  MATH  Google Scholar 

  4. Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Monodirectional P systems. In: Macìas-Ramos, L.F., Păun, G., Riscos-Núñez, A., Valencia-Cabrera, L. (eds.) Proceedings of the 13th Brainstorming Week on Membrane Computing, pp. 207–226. Fénix Editora (2015)

    Google Scholar 

  5. Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Tissue P systems can be simulated efficiently with counting oracles. In: Rozenberg, G., Salomaa, A., Sempere, J.M., Zandron, C. (eds.) CMC 2015. LNCS, vol. 9504, pp. 251–261. Springer, Heidelberg (2015). doi:10.1007/978-3-319-28475-0_17

    Chapter  Google Scholar 

  6. Murphy, N., Woods, D.: The computational power of membrane systems under tight uniformity conditions. Nat. Comput. 10(1), 613–632 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pan, L., Pérez-Jiménez, M.J.: Computational complexity of tissue-like P systems. J. Complex. 26(3), 296–315 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Boston (1993)

    MATH  Google Scholar 

  9. Păun, G.: P systems with active membranes: attacking NP-complete problems. J. Autom. Lang. Comb. 6(1), 75–90 (2001)

    MathSciNet  MATH  Google Scholar 

  10. Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: Complexity classes in models of cellular computing with membranes. Nat. Comput. 2(3), 265–284 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Porreca, A.E., Mauri, G., Zandron, C.: Non-confluence in divisionless P systems with active membranes. Theor. Comput. Sci. 411(6), 878–887 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Păun, G., Pérez-Jiménez, M.J., Riscos Núñez, A.: Tissue P systems with cell division. Int. J. Comput. Commun. Control 3(3), 295–303 (2008)

    Article  Google Scholar 

  13. Sosík, P.: The computational power of cell division in P systems: beating down parallel computers? Nat. Comput. 2(3), 287–298 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sosík, P., Rodríguez-Patón, A.: Membrane computing and complexity theory: a characterization of PSPACE. J. Comput. Syst. Sci. 73(1), 137–152 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zandron, C., Ferretti, C., Mauri, G.: Solving NP-complete problems using P systems with active membranes. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds.) UMC’2K. DISCMATH, pp. 289–301. Springer, Heidelberg (2001). doi:10.1007/978-1-4471-0313-4_21

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milano, Italy

    Alberto Leporati, Luca Manzoni, Giancarlo Mauri, Antonio E. Porreca & Claudio Zandron

Authors
  1. Alberto Leporati
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luca Manzoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giancarlo Mauri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Antonio E. Porreca
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Claudio Zandron
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Claudio Zandron .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca , Milan, Italy

    Alberto Leporati

  2. Leiden University , Leiden, The Netherlands

    Grzegorz Rozenberg

  3. Turku Center for Computer Science , Turku, Finland

    Arto Salomaa

  4. University of Milan-Bicocca , Milan, Italy

    Claudio Zandron

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C. (2017). Shallow Non-confluent P Systems. In: Leporati, A., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. CMC 2016. Lecture Notes in Computer Science(), vol 10105. Springer, Cham. https://doi.org/10.1007/978-3-319-54072-6_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-54072-6_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54071-9

  • Online ISBN: 978-3-319-54072-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation