Algorithm for Application of Evolution Rules Based on Linear Diofantic Equations

Abstract

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.

An Overview of Hardware Implementation of Membrane Computing Models

“…In [45] the set of maximally parallel multisets of rules is expressed as solutions of a system of Diophantine equations (roughly equations (1a) from below) with an additional constraint to be satisfied on a solution, expressed as another system of Diophantine equations. Finally, in [5] the set of maximally parallel multisets of rules can be expressed as solutions to a system of equations defining some Diophantine sets. While the construction is similar to the one we give below, it is not trivial to manipulate Diophantine sets and it is not clear how to express the constraints as a single system of equations.…”

Tele-Treatment Application Design for Disable Patients with Wireless Sensors

“…This proposed project needs a further research on social network [31] and image retrieval in Internet [32] in such a way that they can contribute to it, along with image processing methods [33,34]. In addition, the biomedical data usually has uncertain information [35] that are indeed very helpful for this project [7,[36][37][38][39][40][41][42].…”

Solving complex problems with a bioinspired model

“…Presently, there are some others sequential algorithms for rules application in P-systems (Ciobanu and Paraschiv, 2002;Fernandez et al, 2006b;Arteta et al, 2008) that use different techniques. In particular Arteta et al (2008) use the resolution of linear system diophantine equations to obtain the number of times that rules should be applied.…”

“…In particular Arteta et al (2008) use the resolution of linear system diophantine equations to obtain the number of times that rules should be applied. However, none of these improve the performance of FLA.…”