Advertisement

Systolic Automata and P Systems

  • Roberto Barbuti
  • Andrea Maggiolo-Schettini
  • Paolo Milazzo
  • Giovanni PardiniEmail author
  • Simone Tini
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8808)

Abstract

Systolic automata are models of highly-concurrent language acceptors based on identical processors with one-way flow of information, amenable to efficient hardware implementation as multiprocessor chips.

In this paper we investigate the relationship between Binary Systolic Tree Automata (BSTA), in which the underlying communication structure is an infinite complete binary tree with parallel bottom-up computation, and P systems, a biologically-inspired formalism based on rewrite rules acting upon multisets of symbols with a maximally-parallel semantics.

In particular, we propose a variant of BSTA as multiset languages acceptors, termed Multiset BSTA. By exploiting the similarity in the parallel computation as performed in both BSTA and P systems, we show how a Multiset BSTA can be simulated by a cooperative P system while preserving the computational efficiency of systolic automata.

Keywords

Input Function Processing Function Evolution Rule Special Symbol Compositional Semantic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrei, O., Ciobanu, G., Lucanu, D.: A rewriting logic framework for operational semantics of membrane systems. Theoretical Computer Science 373(3), 163–181 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Barbuti, R., Caravagna, G., Maggiolo-Schettini, A., Milazzo, P.: P systems with endosomes. International Journal of Computers, Communications and Control 4(3), 214–223 (2009)CrossRefzbMATHGoogle Scholar
  3. 3.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Pardini, G.: Simulation of spatial P system models. Theoretical Computer Science 529, 11–45 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Pardini, G., Tesei, L.: Spatial P systems. Natural Computing 10(1), 3–16 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: Compositional semantics and behavioral equivalences for P systems. Theoretical Computer Science 395(1), 77–100 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: A P systems flat form preserving step-by-step behaviour. Fundamenta Informaticae 87(1), 1–34 (2008)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: P systems with transport and diffusion membrane channels. Fundamenta Informaticae 93(1–3), 17–31 (2009)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: Compositional semantics of spiking neural P systems. Journal of Logic and Algebraic Programming 79(6), 304–316 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: Membrane systems working in generating and accepting modes: Expressiveness and encodings. In: Gheorghe, M., Hinze, T., Păun, G., Rozenberg, G., Salomaa, A. (eds.) CMC 2010. LNCS, vol. 6501, pp. 103–118. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: An overview on operational semantics in membrane computing. International Journal of Foundations of Computer Science 22(1), 119–131 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Busi, N.: Using well-structured transition systems to decide divergence for catalytic P systems. Theoretical Computer Science 372(2–3), 125–135 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Csuhaj-Varjú, E., Martín-Vide, C., Mitrana, V.: Multiset Automata. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 69–83. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Culik II, K., Gruska, J., Salomaa, A.: On a family of L languages resulting from systolic tree automata. Theoretical Computer Science 23(3), 231–242 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Culik II, K., Gruska, J., Salomaa, A.: Systolic automata for VLSI on balanced trees. Acta Informatica 18(4), 335–344 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Culik II, K., Gruska, J., Salomaa, A.: Systolic trellis automata I. International Journal of Computer Mathematics 15(1–4), 195–212 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Culik II, K., Gruska, J., Salomaa, A.: Systolic trellis automata II. International Journal of Computer Mathematics 16(1), 3–22 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Culik II, K., Salomaa, A., Wood, D.: Systolic tree acceptors. RAIRO-Theoretical Informatics and Applications-Informatique Théorique et Applications 18(1), 53–69 (1984)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Fachini, E., Gruska, J., Maggiolo-Schettini, A., Sangiorgi, D.: Simulation of systolic tree automata on trellis automata. International Journal of Foundations of Computer Science 1(2), 87–110 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Fachini, E., Maggiolo-Schettini, A., Resta, G., Sangiorgi, D.: Nonacceptability criteria and closure properties for the class of languages accepted by binary systolic tree automata. Theoretical Computer Science 83(2), 249–260 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Fachini, E., Maggiolo-Schettini, A., Sangiorgi, D.: Comparisons among classes of Y-tree systolic automata. In: Rovan, B. (ed.) Mathematical Foundations of Computer Science 1990. LNCS, vol. 452, pp. 254–260. Springer, Berlin Heidelberg (1990)CrossRefGoogle Scholar
  21. 21.
    Fachini, E., Maggiolo-Schettini, A., Sangiorgi, D.: Classes of systolic Y-tree automata and a comparison with systolic trellis automata. Acta Informatica 29(6/7), 623–643 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Gruska, J., Monti, A., Napoli, M., Parente, D.: Succinctness of descriptions of SBTA-languages. Theoretical Computer Science 179(1–2), 251–271 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Păun, G.: Membrane Computing: An Introduction. Springer, Heidelberg (2002)CrossRefzbMATHGoogle Scholar
  24. 24.
    Rozenberg, G., Salomaa, A.: The mathematical theory of L systems. Academic Press (1980)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Roberto Barbuti
    • 1
  • Andrea Maggiolo-Schettini
    • 1
  • Paolo Milazzo
    • 1
  • Giovanni Pardini
    • 1
    Email author
  • Simone Tini
    • 2
  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly
  2. 2.Dipartimento di Scienza e Alta TecnologiaUniversità dell’InsubriaComoItaly

Personalised recommendations