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IMI/Publicaţii/CSJM/Ediţii/CSJM v.18, n.2 (53), 2010/

Minimal Parallelism and Number of Membrane Polarizations

Authors: Alhazov Artiom

Abstract

It is known that the satisfiability problem (SAT) can be efficiently solved by a uniform family of P systems with active membranes with two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is what number of polarizations is sufficient for an efficient computation depending on the types of rules used.
In particular, we show that it is enough to have four polarizations, sequential evolution rules changing polarizations, polarizationless non-elementary membrane division rules and polarizationless rules of sending an object out. The same problem is solved with the standard evolution rules, rules of sending an object out and polarizationless non-elementary membrane division rules, with six polarizations. It is an open question whether these numbers are optimal.

Institute of Mathematics and Computer Science,
Academy of Sciences of Moldova
5 Academiei str., Chişinău, MD 2028, Moldova
E-mail:

FCS, Department of Information Engineering,
Graduate School of Engineering
Hiroshima University,
Higashi-Hiroshima 739-8527 Japan

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