Cell-like P systems with symport/antiport rules are computing models inspired by the conservation law, in the sense that they compute by changing the places of objects with respect to the membranes, and not by changing the objects themselves. In this work, a variant of these kinds of membrane systems, called cell-like P systems with evolutional symport/antiport rules, where objects can evolve in the execution of such rules, is introduced. Besides, inspired by the autopoiesis process (ability of a system to maintain itself), membrane creation rules are considered as an efficient mechanism to provide an exponential workspace in terms of membranes. The presumed efficiency of these computing models (ability to solve computationally hard problems in polynomial time and uniform way) is explored. Specifically, an efficient solution to the SAT problem is provided by means of a family of recognizer cell-like P systems with evolutional symport/antiport rules and membrane creation which make use of communication rules involving a restricted number of objects.

No abstract

Nature-inspired computing is a type of human-designed computing motivated by nature, which is based on the employ of paradigms, mechanisms, and principles underlying natural systems. In this article, a versatile and vigorous bio-inspired branch of natural computing, named membrane computing is discussed. This computing paradigm is aroused by the internal membrane function and the structure of biological cells. We first introduce some basic concepts and formalisms of membrane computing, and then some basic types or variants of P systems (also named membrane systems ) are presented. The state-of-the-art computability theory and a pioneering computational complexity theory are presented with P system frameworks and numerous solutions to hard computational problems (especially NP -complete problems) via P systems with membrane division are reported. Finally, a number of applications and open problems of P systems are briefly described.

a b s t r a c t Keywords:Membrane computing Active membranes Cooperative rules Minimal cooperation Computational complexity The P versus NP problem From a computational complexity point of view, some syntactical ingredients play different roles 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 kind of problems could they solve efficiently In 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.

Cooperation is doubtless a relevant ingredient on rewriting rules based computing models. This paper provides an overview on both classical and newest results studying how cooperation among objects influences the ability of cell-like membrane systems to solve computationally hard problems in an efficient way. In this paper, two types of such membrane systems will be considered: (a) polarizationless P systems with active membranes without dissolution rules when minimal cooperation is permitted in object evolution rules; and (b) cell-like P systems with symport/antiport rules of minimal length. Specifically, assuming that P is not equal to NP, several frontiers of the efficiency are obtained in these two computing frameworks, in such manner that each borderline provides a tool to tackle the P versus NP problem.

P systems with active membranes are usually defined as devices hierarchically structured that evolve through rewriting rules. These rules take the inspiration on the chemical reactions that happen within a cell and the role of both the inner and the plasma membranes as a "filter", letting components pass or not. Classically, these systems are non-cooperative, that is, the left-hand side of the rules has at most one object. Using polarizations, dissolution or cooperation, these systems have been proved to have enough power to efficiently solve computationally hard problems, obtaining new complexity frontiers with respect to their non-cooperative counterparts. In this paper, division rules are interchanged by separation rules. While the first ones produce two new membranes and two new objects, duplicating the objects within the original one, separation rules distribute the objects of the original membrane into the two new created membranes, so no new objects are created in this way. To obtain new objects, a rule of the type [ a → a 2 ] would be needed to accomplish that feature that seems to be necessary to obtain efficient solutions to NP-complete problems. Here, we present the limits when using separation rules instead of division rules.

As with any fast-emerging research front in computer science, the proliferation of theoretical and practical results within Membrane computing since its appearance in 1998 was astonishing. As a consequence, it became necessary during the subsequent years to produce several surveys collecting the main achievements from a theoretical point of view, along with some specific surveys about simulation tools for this paradigm. As the discipline has reached a certain degree of maturity, more practical applications have arisen, and new collective works are summarising the new software products appeared. However, while these recapitulation efforts remain useful for details about new simulators, they cannot act as exhaustive updated listings, as they become obsolete as soon as new tools are developed. Thus, we considered that it was necessary to provide an interactive tool showing an updated timeline (https ://www.gcn.us.es/Simul ation MC) about the simulation of the computational devices of membrane computing (a.k.a P systems), aiming to stay updated whenever any new practical work comes out in the discipline. This paper recalls the main stages and milestones within the evolution of simulation tools for different types and variants of P systems, along with their main related applications. In addition, it describes the interactive web tool with the timeline mentioned, where all the references related here have been incorporated. Unlike other survey papers, it is the intent of this work to reinforce this initial collective effort with the web endpoint kept alive and updated.

In the Membrane Computing area, P systems are unconventional devices of computation inspired by the structure and processes taking place in living cells. Main successful P system applications lie in computability and computational complexity theories, as well as in biological modelling. Given that models become too complex to deal with, simulators for P systems are essential tools and their efficiency is critical. In order to handle the diverse situations that may arise during the computation, these simulators have to take into account that worst-case scenarios can happen, even though they rarely occur. As a result, there is a significant loss of performance. In this paper, the concept of adaptative simulation for P systems is introduced to palliate this problem. This is achieved by passing high-level information provided directly by P system model designers to the simulator, helping it to better adapt to the target model. For this purpose, an existing simulator for an ecosystem modelling framework, named Population Dynamics P systems, is extended to include the information of modules, that are usually employed to define ecosystem models. Moreover, the standard description language for P systems, P-Lingua, has been re-engineered in its version 5. It now includes a new syntactical item, called feature, to express this kind of high-level semantic information. Experiments show that this simple adaptative simulator supporting modules as features doubles the performance when running on GPUs and on multicore processors.