Algorithm for Application of Evolution Rules Based on Linear Diofantic Equations

Transition P system are a parallel and distributed computational model based on the notion of the cellular membrane structure. Each membrane determines a region that encloses a multiset of objects and evolution rules. Transition P systems evolve through transitions between two consecutive configurations. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of evolution rules inside each membrane of the P system. Hence, rules application is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in each one of the evolution steps. It is known that P systems have a high degree of nondeterminism and parallelism. A transition in such a system consists in applying in parallel a set of atomic actions (e.g., evolution rules) and this set of atomic actions is randomly chosen from a domain of possible next transitions. This paper tries to characterize this domain as the hyperspace defined by a set of diophantine equations and then to develop an algorithm which randomly chooses solutions from this hyperspace. Those solutions are uniquely related to the number of times that certain evolution rules are applied. The work presented here includes an algorithm based on resolving linear systems equations and explain into detail the process that the algorithm must follow.