P systems based computing polynomials: design and formal verification

Automatic design of P systems is an attractive research topic in the community of membrane computing. Differing from the previous work that used evolutionary algorithms to fulfill the task, this paper presents the design of a (deterministic transition) P system (without input membrane) of degree 1, capturing the value of an arbitrary k-order () polynomial p(n) by using a reasoning method. Specifically, the values of p(n) corresponding to a natural number t is equal to the multiplicity of a distinguished object of the system (the output object) in the configuration at instant t. We also discuss the descriptive computational resources required by the designed k-order polynomial P system.