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Abstract

We propose a new variant of P systems having as simple as possible evolution rules in which the communication of objects and the membrane dissolving are regulated by a valuation mapping (a morphism which assigns to each word an integer value). Two NP-complete problems are solved by P systems with valuation in linear time.

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References

  1. J. P. Banâtre, A. Coutant, D. Le Metayer, A parallel machine for multiset transformation and its programming style, Future Generation Computer Systems, 4 (1988), 133–144.

    Article  Google Scholar 

  2. R. Constable, H. Hunt, S. Sahni, On the computational complexity of scheme equivalence, Technical Report No. 74-201, Dept. of Computer Science, Cornell University, Ithaca, NY, 1974.

    Google Scholar 

  3. J. Dassow, Gh. Păun, On the power of membrane computing, J. Univ. Computer Sci., 5, 2 (1999),33–49.

    Google Scholar 

  4. M. Garey, D. Johnson, Computers and Intractability. A Guide to the Theory of NP-completeness, Freeman, San Francisco, CA, 1979.

    Google Scholar 

  5. J. Hopcroft, J. Ulmann, Formal Languages and Their Relation to Automata, Addison-Wesley, Reading, MA, 1969.

    MATH  Google Scholar 

  6. L. Kari, G. Gloor, S. Yu, Using DNA to solve the Bounded Correspondence Problem, Theoret. Comput. Sci., 231 (2000), 193–203.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. N. Krishna, R. Rama, A variant of P systems with active membranes: Solving NP-complete problems, Romanian Journal of Information Science and Technology, 2, 4(1999),357–367.

    Google Scholar 

  8. Gh. Păun, A new type of generative devices: valence grammars, Rev. Roum. Math. Pures Appl. 25,6(1980),911–924.

    MATH  Google Scholar 

  9. Gh. Păun, Computing with membranes, J. Comput. Syst. Sci. 61(2000) to apper, (see also TUCS Research Report No. 208, November 1998, http://www.tucs.fi.)

  10. Gh. Păun, Computing with membranes. An introduction, Bulletin of the BATCS, 67 (Febr. 1999),139–152.

    MATH  Google Scholar 

  11. Gh. Păun, Y. Sakakibara, T. Yokomori, P systems on graphs of restricted forms, submitted 1999.

    Google Scholar 

  12. Gh. Păun, T. Yokomori, Membrane computing based on splicing, Preliminary Proc. of Fifth Inter. Meeting on DNA Based Computers (E. Winfree, D. Gifford, eds.), MIT, June 1999,213–227.

    Google Scholar 

  13. Gh. Păun, T. Yokomori, Simulating H systems by P systems, Journal of Universal Computer Science, 6, 1 (2000), 178–193.

    MathSciNet  MATH  Google Scholar 

  14. Gh. Păun, S. Yu, On synchronization in P systems, Fundamenta Inform., 38, 4(1999),397–410.

    MATH  Google Scholar 

  15. Gh. Păun, P systems with active membranes: Attacking NP-complete problems, Journal of Automata, Languages and Combinatorics, in press. (See also CDMTCS Research Report No.102, 1999, Auckland Univ., New Zealand, www.cs.auckland.ac.nz/CDMTCS.)

    Google Scholar 

  16. Gh. Păun, G. Rozenberg, A. Salomaa, DNA Computing. New Computing Paradigms, Springer-Verlag, Berlin, 1998.

    Google Scholar 

  17. Gh. Păun, G. Rozenberg, A. Salomaa, Membrane computing with external output, Fundamenta Inform., 41, 3(2000), 259–266.

    Google Scholar 

  18. G. Rozenberg, A. Salomaa, eds. Handbook of Formal Languages, 3 volumes, Springer, Berlin, 1997.

    MATH  Google Scholar 

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© 2001 Springer-Verlag London

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Martín-Vide, C., Mitrana, V. (2001). P Systems with Valuations. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds) Unconventional Models of Computation, UMC’2K. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0313-4_13

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  • DOI: https://doi.org/10.1007/978-1-4471-0313-4_13

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-415-4

  • Online ISBN: 978-1-4471-0313-4

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