On Nonuniversal Symport/Antiport P Systems

  • Oscar H. IbarraEmail author
  • Sara Woodworth
Part of the Natural Computing Series book series (NCS)


We examine restricted SA P system models and analyze minimal systems with regard to the size of the alphabet and the number of membranes. We study the precise power of SA P systems with either 1, 2, or 3 symbols and less than 5, 4, and 3 membranes, respectively, improving the previous results. The question of whether using only a single symbol with any number of membranes is universal remains open.

We define and examine restricted forms of SA P systems (called bounded SA P systems and special SA P systems) finding infinite hierarchies with respect to the both the size of the alphabet and the number of membranes. We also analyze the role of determinism versus nondeterminism and find that over a unary input alphabet, these systems are equivalent if and only if deterministic and nondeterministic linear-bounded automata (over an arbitrary input alphabet) are equivalent.

Finally, we introduce restricted SA P system models which characterize semilinear sets. We also show “slight” extensions of the models allow them to accept (respectively, generate) nonsemilinear sets. In fact, for these extensions, the emptiness problem is undecidable.


Input Symbol Input Alphabet Skin Membrane System Acceptor Input Counter 
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  1. 1.
    The P systems web page.
  2. 2.
    Alhazov A, Freund R, Oswald M (2005) Symbol/membrane complexity of P systems with symport/antiport rules. In: Proceedings of the 6th international workshop on membrane computing, pp 123–146 Google Scholar
  3. 3.
    Csuhaj-Varju E, Ibarra OH, Vaszil G (2004) On the computational complexity of P automata. In: Proceedings of the 10th international meeting on DNA computing (DNA10). Lecture notes in computer science. Springer, Berlin, pp 97–106 Google Scholar
  4. 4.
    Csuhaj-Varjú E, Martín-Vide C, Mitrana V (2000) Multiset automata. In: Proceedings of the workshop on multiset processing. Lectures notes in computer science, vol 2235. Springer, Berlin, pp 69–84 CrossRefGoogle Scholar
  5. 5.
    Dang Z, Ibarra OH, Li C, Xie G (2005) On model-checking of P systems. In: Proceedings of the 4th international conference on unconventional computation Google Scholar
  6. 6.
    Freund R, Păun G (2003) On deterministic P systems. In: [1] Google Scholar
  7. 7.
    Ginsburg S (1966) The mathematical theory of context-free languages. McGraw–Hill, New York zbMATHGoogle Scholar
  8. 8.
    Greibach S (1978) Remarks on blind and partially blind one-way multicounter machines. Theor Comput Sci 7:311–324 zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hauschildt D, Jantzen M (1994) Petri net algorithms in the theory of matrix grammars. Acta Inform (Hist Arch) 31(8):719–728 zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ibarra OH (1978) Reversal-bounded multicounter machines and their decision problems. J ACM 25:116–133 zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ibarra OH (2005) The number of membranes matters. Theor Comput Sci Google Scholar
  12. 12.
    Ibarra OH (2005) On determinism versus nondeterminism in P systems. Theor Comput Sci Google Scholar
  13. 13.
    Ibarra OH, Woodworth S, Yen H-C, Dang Z (2005) On symport/antiport P systems and semilinear sets. In: Proceedings of the 6th international workshop on membrane computing (WMC6). Lecture notes in computer science. Springer, Berlin, pp 253–271 Google Scholar
  14. 14.
    Ito M, Martín-Vide C, Păun Gh (2001) A characterization of Parikh sets of ETOL languages in terms of P systems. In: Ito M, Păun Gh, Yu S (eds) Words, semigroups, and transductions. Festscrift in honor of Gabriel Thierrin. World Scientific, Singapore, pp 239–253 Google Scholar
  15. 15.
    Martín-Vide C, Pazos J, Păun G, Rodríguez-Patón A (2003) Tissue P systems. Theor Comput Sci 296(2):295–326 zbMATHCrossRefGoogle Scholar
  16. 16.
    Minsky M (1961) Recursive unsolvability of Post’s problem of tag and other topics in the theory of Turing machines. Ann Math 74:437–455 CrossRefMathSciNetGoogle Scholar
  17. 17.
    Monien B (1980) Two-way multihead automata over a one-letter alphabet. RAIRO Inform Theor 14(1):67–82 zbMATHMathSciNetGoogle Scholar
  18. 18.
    Păun A, Păun G (2006) The power of communication: P systems with symport/antiport. New Gener Comput 20(3):295–306 CrossRefGoogle Scholar
  19. 19.
    Păun G, Pazos J, Pérez-Jiménez MJ, Rodríguez-Patón A (2005) Symport/antiport P systems with three objects are universal. Fundam Inform 64(1–4):353–367 zbMATHGoogle Scholar
  20. 20.
    Savitch W (1970) Relationships between nondeterministic and deterministic tape complexities. J Comput Syst Sci 4(2):177–192 zbMATHMathSciNetGoogle Scholar
  21. 21.
    Savitch W (1973) A note on multihead automata and context-sensitive languages. Acta Inform 2:249–252 zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Sosík P (2002) P systems versus register machines: two universality proofs. In: Proceedings of workshop on membrane computing (WMC-CdeA2002), pp 371–382 Google Scholar

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

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