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On Nonuniversal Symport/Antiport P Systems

  • Oscar H. IbarraEmail author
  • Sara Woodworth
Chapter
Part of the Natural Computing Series book 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.

Keywords

Input Symbol Input Alphabet Skin Membrane System Acceptor Input Counter 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

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