We present the first membrane computing solution to the Subset-Sum problem using a family of deterministic P systems with active membranes. We do not use priority among rules, membrane dissolution nor cooperation; it suffices to control the electrical charges of the membranes and to introduce some counters. The number of steps of any computation is of the linear order (but it is necessary a polynomial-time of precomputed resources).
Many NP-complete problems can be viewed as special cases
of the Common Algorithmic Problem (CAP). In a precise sense, which
will be defined in the paper, one may say that CAP has a property of
local universality. In this paper we present an effective solution to the
decision version of the CAP using a family of recognizer P systems with
active membranes. The analysis of the solution presented here will be
done from the point of view of complexity classes in P systems.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
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