Miguel A. Gutiérrez-Naranjo

A uniform family of tissue P systems with cell division solving 3-COL in a linear time

Several examples of the efficiency of cell-like P systems regarding the solution of NP-complete problems in polynomial time can be found in the literature(obviously, trading space for time). Recently, different new models of tissue-like P systems have received much attention from the scientific community. In this paper we present a linear-time solution to an NP-complete problem from graph theory, the 3-coloring problem, and we discuss the suitability of tissue-like P systems as a framework to address the efficient solution to intractable problems.

A fast P system for finding a balanced 2-partition

Numerical problems are not very frequently addressed in the P systems literature. In this paper we present an effective solution to the 2-Partition problem via a family of deterministic P systems with active membranes using 2-division. The design of this solution is a sequel of several previous works on other problems, mainly on the Subset-Sum and the Knapsack problems. Several improvements are introduced and explained.

Solving Subset Sum in Linear Time by Using Tissue P Systems with Cell Division

Tissue P systems with cell division is a computing model in the framework of Membrane Computing based on intercellular communication and cooperation between neurons. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to NP -complete problems in polynomial time. In this paper we present a solution to the Subset Sum problem via a family of such devices. This is the first solution to a numerical NP -complete problem by using tissue P systems with cell division.

Available Membrane Computing Software

The simulation of a P system with current computers is a quite complex task. P systems are intrinsically nondeterministic computational devices and therefore their computation trees are difficult to store and handle with computers with one processor (or a bounded number of processors). Nevertheless, there exists a first generation of simulators which can be successfully used for pedagogical purposes and as assistant tools for researchers. This chapter summarizes some of these simulators, presenting the state of the art of the available software for simulating (different variants of) cell-like membrane systems.

Segmenting images with gradient-based edge detection using Membrane Computing

In this paper, we present a parallel implementation of a new algorithm for segmenting images with gradient-based edge detection by using techniques from Natural Computing. This bio-inspired parallel algorithm has been implemented in a novel device architecture called CUDA(TM)(Compute Unified Device Architecture). The implementation has been designed via tissue P systems on the framework of Membrane Computing. Some examples and experimental results are also presented.

Computational efficiency of dissolution rules in membrane systems

Trading (in polynomial time) space for time in the framework of membrane systems is not sufficient to efficiently solve computationally hard problems. On the one hand, an exponential number of objects generated in polynomial time is not sufficient to solve NP-complete problems in polynomial time. On the other hand, when an exponential number of membranes is created and used as workspace, the situation is very different. Two operations in P systems (membrane division and membrane creation) capable of constructing an exponential number of membranes in linear time are studied in this paper. NP-complete problems can be solved in polynomial time using P systems with active membranes and with polarizations, but when electrical charges are not used, then dissolution rules turn out to be very important. We show that in the framework of P systems with active membranes but without polarizations and in the framework of P systems with membrane creation, dissolution rules play a crucial role from the computational efficiency point of view.

A Linear--time Tissue P System Based Solution for the 3--coloring Problem

In the literature, several examples of the efficiency of cell-like P systems regarding the solution of NP-complete problems in polynomial time can be found (obviously, trading space for time). Recently, different new models of tissue-like P systems have received important attention from the scientific community. In this paper we present a linear-time solution to an NP-complete problem from graph theory, the 3-coloring problem, and we discuss the suitability of tissue-like P systems as a framework to address the efficient solution to intractable problems.

A linear solution for QSAT with membrane creation

The usefulness of P systems with membrane creation for solving NP problems has been previously proved (see [2, 3]), but, up to now, it was an open problem whether such P systems were able to solve PSPACE-complete problems in polynomial time. In this paper we give an answer to this question by presenting a uniform family of P system with membrane creation which solves the QSAT-problem in linear time.

A parallel algorithm for skeletonizing images by using spiking neural P systems

Abstract Skeletonization is a common type of transformation within image analysis. In general, the image B is a skeleton of the black and white image A , if the image B is made of fewer black pixels than the image A , it does preserve its topological properties and, in some sense, keeps its meaning . In this paper, we aim to use spiking neural P systems (a computational model in the framework of membrane computing) to solve the skeletonization problem. Based on such devices, a parallel software has been implemented within the Graphics Processors Units (GPU) architecture. Some of the possible real-world applications and new lines for future research will be also dealt with in this paper.

Towards a Programming Language in Cellular Computing

Several solutions to hard numerical problems using P systems have been presented recently, and strong similarities in their designs have been noticed. In this paper we present a new solution, to the Partition problem, via a family of deterministic P systems with active membranes using 2-division. Then, we intend to show that the idea of a cellular programming language is possible (at least for some relevant family of NP-complete problems), indicating some “subroutines” that can be used in a variety of situations and therefore could be useful for designing solutions for new problems in the future.