Solving Problems in a DistributedWay in Membrane Computing: dP Systems

Abstract

Although P systems are distributed parallel computing devices, no explicit way of handling the input in a distributed way in this framework was considered so far. This note proposes a distributed architecture (based on cell-like P systems, with their skin membranes communicating through channels as in tissue-like P systems, according to specified rules of the antiport type), where parts of a problem can be introduced as inputs in various components and then processed in parallel. The respective devices are called dP systems, with the case of accepting strings called dP automata. The communication complexity can be evaluated in various ways: statically (counting the communication rules in a dP system which solves a given problem), or dynamically (counting the number of communication steps, of communication rules used in a computation, or the number of objects communicated). For each measure, two notions of "parallelizability" can be introduced. Besides (informal) definitions, some illustrations of these idea are provided for dP automata: each regular language is "weakly parallelizable" (i.e., it can be recognized in this framework, using a constant number of communication steps), and there are languages of various types with respect to Chomsky hierarchy which are "efficiently parallelizable" (they are parallelizable and, moreover, are accepted in a faster way by a dP automaton than by a single P automaton). Several suggestions for further research are made.

Membrane parallelism for discrete Morse theory applied to digital images

“…The chosen P system model for our framework is based in the works of Pȃun and Pérez-Jiménez in [26]. Here, a finite set of tissue like P systems working in a cooperative way is used, where each of them solves a part of the problem and, in some conditions, sends each output to other P system to be processed by it.…”

Membrane Computing—A Quick Survey

“…[40], synthesized in a unique theorem: Extended here means to have a subset T ⊆ O and to ignore the objects from O − T , keeping in the recognized string only the elements of T .…”

“…Only a few more precise definitions and results were provided, for a recent class of P systems, the distributed ones, introduced in Ref. [40] in the aim of providing a framework for communication complexity investigations in the sense of Ref. [28].…”

The P System Design Method based on the P Module

“…In 2009, Romero-Campero et al proposed a biology model for modular combination cells [15] and Serbanuta et al proposed K systems embedded in P system which can develop new extensions of P system [16]. In 2010, Pȃun et al proposed the dp system [17], which contains ideas for modularity.…”