Static Analysis of Usefulness States in Transition P Systems

Transition P Systems 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 that are determined by the membrane structure and multisets present inside membranes. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of evolution rules. But, to establish the rules to be applied, it is required the previous calculation of useful, applicable and active rules. Hence, computation of useful evolution rules is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in every evolution step. This work defines usefulness states through an exhaustive analysis of the P system for every membrane and for every possible configuration of the membrane structure during the computation. Moreover, this analysis can be done in a static way; therefore membranes only have to check their usefulness states to obtain their set of useful rules during execution.

Mathematical Modeling of the Weaving Structure Design

Красимир Йорджев, Христина Костадинова - В работата се разглежда една релация на еквивалентност в множеството от всички квадратни бинарни матрици. Обсъдена е комбинаторната задача за намиране мощността и елементите на фактормножеството относно тази релация. Разгледана е и възможността за получаване на някои специални елементи на това фактормножество. Предложен е алгоритъм за решаване на поставените задачи. Получените в статията резултати намират приложение при описанието топологията на различните тъкачни структури.