Search

Biological membranes play an active role in the evolution of cells over time. In the framework of Membrane Computing, P systems with active membranes capture this idea, and the possibility to increase the number of membranes during a computation. Classically, it has been considered, by using division rules, inspired in the mitosis process. Initially, the membranes in these models are supposed to have an electrical polarization (positive, negative or neutral) and the semantics is minimalist, in the sense that rules are applied in parallel, but in one transition step, each membrane can be the subject of at most one rule of types communication, dissolution or division. This paper focuses on polarizationless P systems with active membranes in which membrane creation rules are considered instead of membrane division rules as a mechanism to construct an exponential workspace, expressed both in terms of number of objects and membranes, in linear time. Moreover, the minimalist semantics is considered and some complexity results are provided in this framework, allowing to tackle the PversusNP problem from a new perspective. An original frontier of the efficiency in this context is unveiled in this paper: allowing membrane creation rules to be applicable in any membrane of the system, instead of restricting them to only elementary membranes, yields a significant boost on the computational power. More precisely, only problems in P can be efficiently solved in the restricted case, while in the non-restricted case an efficient and uniform solution to a PSPACE-complete problem is provided. [ABSTRACT FROM AUTHOR]

Membrane computing is a computing paradigm providing a class of distributed parallel computing devices of a biochemical type whose process units represent biological membranes. In the cell-like basic model, a hierarchical membrane structure formally described by a rooted tree is considered. It is well known that families of such systems where the number of membranes can only decrease during a computation (for instance by dissolving membranes), can only solve in polynomial time problems in class P. P systems with active membranes is a variant where membranes play a central role in their dynamics. In the seminal version, membranes have an electrical polarization (positive, negative, or neutral) associated in any instant, and besides being dissolved, they can also replicate by using division rules. These systems are computationally universal, that is, equivalent in power to deterministic Turing machines, and computationally efficient, that is, able to solve computationally hard problems in polynomial time. If polarizations in membranes are removed and dissolution rules are forbidden, then only problems in class P can be solved in polynomial time by these systems (even in the case when division rules for non-elementary membranes are permitted). In that framework it has been shown that by considering minimal cooperation (left-hand side of such rules consists of at most two symbols) and minimal production (only one object is produced by the application of such rules) in object evolution rules, such systems provide efficient solutions to NP-complete problems. In this paper, minimal cooperation and minimal production in communication rules instead of object evolution rules is studied, and the computational efficiency of these systems is obtained in the case where division rules for non-elementary membranes are permitted. [ABSTRACT FROM AUTHOR]

Sevilla carpets have already been used to compare different solutions of the Subset Sum problem: either designed in the framework of P systems with active membranes (both in the case of membrane division and membrane creation), and in the framework of tissue-like P systems with cell division. Recently, the degree of parallelism and other descriptive complexity details have been found to be relevant when designing parallel simulators running on GPUs. We present here a new way to use the information provided by Sevilla carpets in this context, and a script that allows to generate them automatically from P-Lingua files. [ABSTRACT FROM AUTHOR]

In 1936 A. Turing showed the existence of a universal machine able to simulate any Turing machine given its description. In 1956, C. Shannon formulated for the first time the problem of finding the smallest possible universal Turing machine according to some critera to measure its size such as the number of states and symbols. Within the framework of Membrane Computing different studies have addressed this problem: small universal symport/antiport P systems (by considering the number of membranes, the weight of the rules and the number of objects as a measure of the size of the system), small universal splicing P systems (by considering the number of rules as a measure of the size of the system), and small universal spiking neural P systems (by considering the number of neurons as a measure of the size of the system). In this paper the problem of determining the smallest possible efficient P system is explicitly formulated. Efficiency within the framework of Membrane Computing refers to the capability of solving computationally hard problems (i.e. problems such that classical electronic computer cannot solve instances of medium/large size in any reasonable amount of time) in polynomial time. A descriptive measure to define precisely the notion of small P system is presented in this paper. [ABSTRACT FROM AUTHOR]