On symport/antiport p systems and semilinear sets

Authors:
Oscar H. Ibarra;Sara Woodworth;Hsu-Chun Yen;Zhe Dang
Affiliations:
Department of Computer Science, University of California, Santa Barbara, CA;Department of Computer Science, University of California, Santa Barbara, CA;Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, R.O.C;School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA
Venue:
WMC'05 Proceedings of the 6th international conference on Membrane Computing
Year:
2005

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Abstract

We introduce some restricted models of symport/antiport P systems that are used as acceptors (respectively, generators) of sets of tuples of non-negative integers and show that they characterize precisely the semilinear sets. Specifically, we prove that a set R⊆ Nk is accepted (respectively, generated) by a restricted system if and only if R is a semilinear set. We also show that “slight” extensions of the models will allow them to accept (respectively, generate) non-semilinear sets. In fact, for these extensions, the emptiness problem is undecidable.