Skip to main content
SpringerLink
Log in
Book cover

Algorithmic Bioprocesses pp 229–272Cite as

On Nonuniversal Symport/Antiport P Systems

  • Chapter
  • First Online:

  • 1235 Accesses

Part of the book series: Natural Computing Series ((NCS))

Abstract

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.

This work was supported in part by NSF Grants CCF-0430945 and CCF-052416.

This is a preview of subscription content, 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   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. The P systems web page. http://psystems.disco.unimib.it

  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. 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. 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

    Chapter  Google Scholar 

  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. Freund R, Păun G (2003) On deterministic P systems. In: [1]

    Google Scholar 

  7. Ginsburg S (1966) The mathematical theory of context-free languages. McGraw–Hill, New York

    MATH  Google Scholar 

  8. Greibach S (1978) Remarks on blind and partially blind one-way multicounter machines. Theor Comput Sci 7:311–324

    Article  MATH  MathSciNet  Google Scholar 

  9. Hauschildt D, Jantzen M (1994) Petri net algorithms in the theory of matrix grammars. Acta Inform (Hist Arch) 31(8):719–728

    Article  MATH  MathSciNet  Google Scholar 

  10. Ibarra OH (1978) Reversal-bounded multicounter machines and their decision problems. J ACM 25:116–133

    Article  MATH  MathSciNet  Google Scholar 

  11. Ibarra OH (2005) The number of membranes matters. Theor Comput Sci

    Google Scholar 

  12. Ibarra OH (2005) On determinism versus nondeterminism in P systems. Theor Comput Sci

    Google Scholar 

  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. 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. Martín-Vide C, Pazos J, Păun G, Rodríguez-Patón A (2003) Tissue P systems. Theor Comput Sci 296(2):295–326

    Article  MATH  Google Scholar 

  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

    Article  MathSciNet  Google Scholar 

  17. Monien B (1980) Two-way multihead automata over a one-letter alphabet. RAIRO Inform Theor 14(1):67–82

    MATH  MathSciNet  Google Scholar 

  18. Păun A, Păun G (2006) The power of communication: P systems with symport/antiport. New Gener Comput 20(3):295–306

    Article  Google Scholar 

  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

    MATH  Google Scholar 

  20. Savitch W (1970) Relationships between nondeterministic and deterministic tape complexities. J Comput Syst Sci 4(2):177–192

    MATH  MathSciNet  Google Scholar 

  21. Savitch W (1973) A note on multihead automata and context-sensitive languages. Acta Inform 2:249–252

    Article  MATH  MathSciNet  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra & Sara Woodworth

Authors
  1. Oscar H. Ibarra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sara Woodworth
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oscar H. Ibarra .

Editor information

Editors and Affiliations

  1. Dept. Computer Science, University of British Columbia, Main Mall 201-2366, Vancouver, V6T 1Z4, Canada

    Anne Condon

  2. Dept. Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    David Harel

  3. Leiden Inst. Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands

    Joost N. Kok

  4. Turku Centre for Computer Science, Lemminkaisenkatu 14 A, Turku, 20520, Finland

    Arto Salomaa

  5. Computer Science, Computation,, California Inst. of Technology, Pasadena, 91125, U.S.A.

    Erik Winfree

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ibarra, O.H., Woodworth, S. (2009). On Nonuniversal Symport/Antiport P Systems. In: Condon, A., Harel, D., Kok, J., Salomaa, A., Winfree, E. (eds) Algorithmic Bioprocesses. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88869-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88869-7_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88868-0

  • Online ISBN: 978-3-540-88869-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation