P Systems based Computing Polynomials with Integer Coefficients: Design and Formal Verification

Abstract

Automatic design of membrane computing models is an im- portant and useful research topic in the area of membrane computing. Following the previous work that a polynomial P system with natural number coefficients, this paper proposes the design of a deterministic transition P system (with priorities and without input membrane) of degree 1, capturing the value of an arbitrary k-degree (k ≥ 2) poly- nomial p(n) with integer coefficients. To be specific, the values of p(n) corresponding to a natural number t is equal to the multiplicity (with a positive or negative sign) of a distinguished object of the system (the output object) in the configuration at instant t. The descriptive compu- tational resources required by the designed k-degree polynomial P system are also discussed