P Systems with Active Membranes and Separation Rules

The P systems are a class of distributed parallel computing devices of a biochemical type. In this paper, a new de¯nition of separation rules in P systems with active membranes is given. Under the new de¯nition, the e±ciency and universality of P systems with active membranes and separation rules instead of division are investigated

A new perspective on computational complexity theory in Membrane Computing

A single Turing machine can solve decision problems with an in nite number of instances. On the other hand, in the framework of membrane computing, a \solution" to an abstract decision problem consists of a family of membrane systems (where each system of the family is associated with a nite set of instances of the problem to be solved). An interesting question is to analyze the possibility to nd a single membrane system able to deal with the in nitely many instances of a decision problem. In this context, it is fundamental to de ne precisely how the instances of the problem are introduced into the system. In this paper, two different methods are considered: pre-computed (in polynomial time) resources and non-treated resources. An extended version of this work will be presented in the 20th International Conference on Membrane Computing.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

A syntax for semantics in P-Lingua

P-Lingua is a software framework for Membrane Computing, it includes a programming language, also called P-Lingua, for writting P system de nitions using a syntax close to standard scienti c notation. The rst line of a P-Lingua le is an unique identi er de ning the variant or model of P system to be used, i.e, the semantics of the P system. Software tools based on P-Lingua use this identi er to select a simulation algorithm implementing the corresponding derivation mode. Derivation modes de ne how to obtain a con guration Ct+1 from a con guration Ct. This information is usually hard-coded in the simulation algorithm. The P system model also de nes what types or rules can be used, the P-Lingua compiler uses the identi er to select an speci c parser for the le. In this case, a set of parsers is codi ed within the compiler tool. One for each unique identi er. P-Lingua has grown during the last 12 years, including more and more P system models. From a software engineering point of view, this approximation implies a continous development of the framework, leading to a monolithic software which is hard to debug and maintain. In this paper, we propose a new software approximation for the framework, including a new syntax for de ning rule patterns and derivation modes. The P-Lingua users can now de ne custom P system models instead of hard-coding them in the software. This approximation leads to a more exible solution which is easier to maintain and debug. Moreover, users could de ne and play with new/experimental P system models

An apparently innocent problem in Membrane Computing

The search for effcient solutions of computationally hard problems by means of families of membrane systems has lead to a wide and prosperous eld of research. The study of computational complexity theory in Membrane Computing is mainly based on the look for frontiers of effciency between different classes of membrane systems. Every frontier provides a powerful tool for tackling the P versus NP problem in the following way. Given two classes of recognizer membrane systems R1 and R2, being systems from R1 non-effcient (that is, capable of solving only problems from the class P) and systems from R2 presumably e cient (that is, capable of solving NP-complete problems), and R2 the same class that R1 with some ingredients added, passing from R1 to R2 is comparable to passing from the non effciency to the presumed effciency. In order to prove that P = NP, it would be enough to, given a solution of an NP-complete problem by means of a family of recognizer membrane systems from R2, try to remove the added ingredients to R2 from R1. In this paper, we study if it is possible to solve SAT by means of a family of recognizer P systems from AM0(�����d;+n), whose non-effciency was demonstrated already

Limits on P Systems with Proteins and Without Division

In the field of Membrane Computing, computational complexity theory has been widely studied trying to nd frontiers of efficiency by means of syntactic or semantical ingredients. The objective of this is to nd two kinds of systems, one non-efficient and another one, at least, presumably efficient, that is, that can solve NP-complete prob- lems in polynomial time, and adapt a solution of such a problem in the former. If it is possible, then P = NP. Several borderlines have been defi ned, and new characterizations of different types of membrane systems have been published. In this work, a certain type of P system, where proteins act as a supporting element for a rule to be red, is studied. In particular, while division rules, the abstraction of cellular mitosis is forbidden, only problems from class P can be solved, in contrast to the result obtained allowing them.Ministerio de Economía y Competitividad TIN2017-89842-PNational Natural Science Foundation of China No 6132010600

Reaching efficiency through collaboration in membrane systems: Dissolution, polarization and cooperation

From a computational complexity point of view, some syntactical ingredients play differentroles depending on the kind of combination considered. Inspired by the fact that the passing of a chemical substance through a biological membrane is often done by an interaction with the membrane itself, systems with active membranes were considered.Several combinations of different ingredients have been used in order to know which kindof problems could they solve efficientlyIn this paper, minimal cooperation with a minimal expression (the left-hand side of every object evolution rule has at most two objects and its right-hand side contains only one object) in object evolution rules is considered and a polynomial-time uniform solution to the SAT problem is presented. Consequently, a new way to tackle the P versus NP problem is provided.National Natural Science Foundation of China No 61472328National Natural Science Foundation of China No 6132010600

Membrane Fission: A Computational Complexity Perspective

Membrane fission is a process by which a biological membrane is split into two new ones in the manner that the content of the initial membrane is separated and distributed between the new membranes. Inspired by this biological phenomenon, membrane separation rules were considered in membrane computing. In this work, we investigate cell-like P systems with symport/antiport rules and membrane separation rules from a computational complexity perspective. Specifically, we establish a limit on the efficiency of such P systems which use communication rules of length at most two, and we prove the computational efficiency of this kind of models when using communication rules of length at most three. Hence, a sharp borderline between tractability and NP–hardness is provided in terms of the length of communication rules.Ministerio de Economía y Competitividad TIN2012-3743

Solving Problems Through a Single Membrane System

The tape of a deterministic Turing machine contains an unbounded number of cells. Thanks to that, a single machine can solve decision problems with an infinite number of instances. Nevertheless, in the framework of membrane computing, traditionally a \solution" to an abstract decision problem consists of a family of membrane systems (where each system of the family is associated with a finite set of instances of the problem to be solved). An interesting question is to analyze the possibility to find a single membrane system able to deal with the infinitely many instances of a decision problem. In this context, it is fundamental to define precisely how the instances of the problem are introduced into the system. In this paper, two different methods are considered. The first one relies on a pre-computing process, where a polynomial-time computable function will be in charge of producing a multiset of objects associated with the instance to be solved. On the other hand, the second one assumes that the input alphabet of the system is equal to the alphabet of instances, and therefore instances are directly introduced in the initial configuration of the system. Polynomial complexity classes associated with these two approaches are introduced and some complexity aspects are studied.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

Limits of the power of Tissue P systems with cell division

Tissue P systems generalize the membrane structure tree usual in original models of P systems to an arbitrary graph. Basic opera- tions in these systems are communication rules, enriched in some variants with cell division or cell separation. Several variants of tissue P systems were recently studied, together with the concept of uniform families of these systems. Their computational power was shown to range between P and NP ? co-NP , thus characterizing some interesting borderlines between tractability and intractability. In this paper we show that com- putational power of these uniform families in polynomial time is limited by the class PSPACE . This class characterizes the power of many clas- sical parallel computing model