[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Sequential and maximally parallel multiset rewriting: reversibility and determinism

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

We study reversibility and determinism aspects and the strong versions of these properties of sequential multiset processing systems and of maximally parallel systems, from the computability point of view. In the sequential case, syntactic criteria are established for both strong determinism and strong reversibility. In the parallel case, a criterion is established for strong determinism, whereas strong reversibility is shown to be decidable. In the sequential case, without control all four classes—deterministic, strongly deterministic, reversible, strongly reversible—are not universal, whereas in the parallel case deterministic systems are universal. When allowing inhibitors, the first and the third class become universal in both models, whereas with priorities all of them are universal. In the maximally parallel case, strongly deterministic systems with both promoters and inhibitors are universal. We also present a few more specific results and conjectures.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Alhazov A, Freund R, Morita K (2010) Reversibility and determinism in sequential multiset rewriting. In: Calude CS, Hagiya M, Morita K, Rozenberg G, Timmis J (eds) Unconventional computation 2010, Tokyo. Lecture notes in computer science, vol 6079. Springer, New York, pp 21–31

  • Alhazov A, Morita K (2010) On reversibility and determinism in P systems. In: Păun G, Pérez-Jiménez MJ, Riscos-Núñez A, Rozenberg G, Salomaa A (eds) Membrane computing, 10th international workshop, WMC 2009, Curtea de Argeş, revised selected and invited papers. Lecture notes in computer science, vol 5957. pp 158–168

  • Bennett CH (1973) Logical reversibility of computation. IBM J Res Dev 17:525–532

    Article  MATH  Google Scholar 

  • Calude CS, Păun Gh (2004) Bio-steps beyond Turing. BioSystems 77:175–194

    Article  Google Scholar 

  • Dassow J, Păun Gh (1989) Regulated rewriting in formal language theory. In: EATCS monographs in theoretical computer science, vol 18. Springer, New York

  • Fredkin E, Toffoli T (1982) Conservative logic. Int J Theor Phys 21:219–253

    Article  MATH  MathSciNet  Google Scholar 

  • Freund R, Ibarra OH, Păun Gh, Yen H-C (2005) Matrix Languages, Register Machines, Vector Addition Systems. In: Gutiérrez-Naranjo MA, Riscos-Núñez A, Romero-Campero FJ, Sburlan D (eds) RGNC report 01/2005. Third brainstorming week on membrane computing. University of Seville, Fénix Editora, Sevilla, pp 155–168

  • Ibarra OH (2011) On strong reversibility in P systems and related problems. Int J Found Comput Sci 22(1):7–14

    Google Scholar 

  • Leporati A, Zandron C, Mauri G (2006) Reversible P systems to simulate Fredkin circuits. Fundam Inform 74(4):529–548

    MATH  MathSciNet  Google Scholar 

  • Minsky ML (1969) Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs

  • Morita K (1996) Universality of a reversible two-counter machine. Theor Comput Sci 168:303–320

    Article  MATH  Google Scholar 

  • Morita K (2001) A simple reversible logic element and cellular automata for reversible computing. In: Margenstern M, Rogozhin Yu (eds) Proceedings of 3rd international conference on machines, computations, and universality. Lecture notes in computer science, vol 2055. Springer, New York. pp 102–113

  • Morita K (2007) Simple universal one-dimensional reversible cellular automata. J Cell Autom 2:159–165

    MATH  MathSciNet  Google Scholar 

  • Morita K, Nishihara N, Yamamoto Y, Zhang Zh (1997) A hierarchy of uniquely parsable grammar classes and deterministic acceptors. Acta Inform 34(5):389–410

    Article  MathSciNet  Google Scholar 

  • Morita K, Yamaguchi Y (2007) A universal reversible turing machine. In: Proceedings of 5th international conference on machines, computations, and universality. Lecture notes in computer science, vol 4664. Springer, New York, pp 90–98

  • Păun Gh (2002) Membrane computing. An Introduction. Springer, Berlin

    Book  MATH  Google Scholar 

  • P Systems Webpage. http://ppage.psystems.eu/

Download references

Acknowledgments

Artiom Alhazov gratefully acknowledges the support of the Japan Society for the Promotion of Science and the Grant-in-Aid for Scientific Research, project \(20\cdot08364\). He also acknowledges the support by the Science and Technology Center in Ukraine, project 4032.

Author information

Authors and Affiliations

  1. FCS, Department of Information Engineering, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Artiom Alhazov & Kenichi Morita

  2. Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academiei 5, Chişinău, 2028, Moldova

    Artiom Alhazov

  3. Faculty of Informatics, Vienna University of Technology, Favoritenstr. 9, 1040, Vienna, Austria

    Rudolf Freund

Authors
  1. Artiom Alhazov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rudolf Freund
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kenichi Morita
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Artiom Alhazov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alhazov, A., Freund, R. & Morita, K. Sequential and maximally parallel multiset rewriting: reversibility and determinism. Nat Comput 11, 95–106 (2012). https://doi.org/10.1007/s11047-011-9267-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-011-9267-8

Keywords

Search

Navigation