Tuning Frontiers of Efficiency in Tissue P Systems with Evolutional Communication Rules

Abstract

Over the last few years, a new methodology to address the P versus NP problem has been developed, based on searching for borderlines between the nonefficiency of computing models (only problems in class P can be solved in polynomial time) and the presumed efficiency (ability to solve NP-complete problems in polynomial time). These borderlines can be seen as frontiers of efficiency, which are crucial in this methodology. “Translating,” in some sense, an efficient solution in a presumably efficient model to an efficient solution in a nonefficient model would give an affirmative answer to problem P versus NP. In the framework of Membrane Computing, the key of this approach is to detect the syntactic or semantic ingredients that are needed to pass from a nonefficient class of membrane systems to a presumably efficient one. This paper deals with tissue P systems with communication rules of type symport/antiport allowing the evolution of the objects triggering the rules. In previous works, frontiers of efficiency were found in these kinds of membrane systems both with division rules and with separation rules. However, since they were not optimal, it is interesting to refine these frontiers. In this work, optimal frontiers of the efficiency are obtained in terms of the total number of objects involved in the communication rules used for that kind of membrane systems. These optimizations could be easier to translate, if possible, to efficient solutions in a nonefficient model.

P Systems with Evolutional Communication and Division Rules

“…In the generation stage, different elements necessary for the rest of the computation are generated at the same time. First, in order to avoid the use of the environment to obtain γ objects, it is necessary to use some of the synchronization protocols in [32], 2 np+2 copies of the object γ np+2 will be generated in membranes np + 5 through the rules from 6.1. These objects will be present in the membrane np + 1 at configuration C np+3 .…”

“…In [29], several new results were presented, publishing some improvements from [28,[30][31][32]. More precisely, in [32] an efficient family of tissue P systems with evolutional communication rules of length at most (2, 1) and division rules using the environment as an active agent of the system solving the SAT problem is presented.…”

“…In [29], several new results were presented, publishing some improvements from [28,[30][31][32]. More precisely, in [32] an efficient family of tissue P systems with evolutional communication rules of length at most (2, 1) and division rules using the environment as an active agent of the system solving the SAT problem is presented. In this work, we investigate the role of evolutional communication rules in cell-like membrane systems that use division rules as exponential workspace-generating rules, and letting the environment as a mere agent that only receives the corresponding answer of the system.…”

P systems with evolutional symport and membrane creation rules solving QSAT

“…In [18], a new variant of tissue P systems was introduced, where symport/antiport rules allow objects to evolve in the process of the communication from a region to another region. Some relevant results have been obtained in [19][20][21][22], where some frontiers of efficiency have been obtained. In the framework of cell-like membrane systems, creation rules have been used lately besides evolutional communication rules in [23] to solve the SAT problem by means of a family of recognizer P systems with evolutional communication rules and creation rules.…”