P Systems-Based Computing Polynomials With Integer Coefficients: Design and Formal Verification

Automatic design of mechanical procedures solving abstract problems is a relevant scientific challenge. In particular, automatic design of membranes systems performing some prefixed tasks is an important and useful research topic in the area of Natural Computing. In this context, deterministic membrane systems were designed in order to capture the values of polynomials with natural numbers coefficients. Following that work, this paper extends the previous result to polynomials with integer numbers coefficients. Specifically, a deterministic transition P system using priorities in the weak interpretation, associated with an arbitrary such kind polynomial, is presented. The configuration of the unique computation of the system will be encoded by means of two distinguished objects, the values of the polynomial for natural numbers. The descriptive computational resources required by the designed membrane system are also analyzed.