David Orellana-Martín

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

Abstract 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.

From distribution to replication in cooperative systems with active membranes: A frontier of the efficiency

Abstract P systems with active membranes use evolution, communication, dissolution and division (or separation) rules. They do not use cooperation neither priorities, but they have electrical charges associated with membranes, which can be modified by rule applications. The inspiration comes from the behaviour of living cells, who “compute” with their proteins in order to obtain energy, create components, send information to other cells, kill themselves (in a process called apoptosis), and so on. In these models, mitosis is simulated by division rules (for elementary and non-elementary membranes) and meiosis, that is, membrane fission inspiration, is captured in separation rules. The parents objects are replicated into both child membranes when a division occurs, while in the case of separation, objects are distributed (according to a prefixed partition). In both cases, active membranes have been proved to be too powerful for solving computationally hard problems in an efficient way. Due to this, polarizationless P systems with active membranes have been widely studied from a complexity point of view. Evolution rules simulate the transformation of components in membranes, but it is well known that in Biology elements interact with each other in order to obtain new components. In this paper, (restricted) cooperation in object evolution rules is considered, and the efficiency of the corresponding models is studied.

Counting Membrane Systems

A decision problem is one that has a yes/no answer, while a counting problem asks how many possible solutions exist associated with each instance. Every decision problem X has associated a counting problem, denoted by \(\# X\), in a natural way by replacing the question “is there a solution?” with “how many solutions are there?”. Counting problems are very attractive from a computational complexity point of view: if X is an NP-complete problem then the counting version \(\# X\) is NP-hard, but the counting version of some problems in class P can also be NP-hard. In this paper, a new class of membrane systems is presented in order to provide a natural framework to solve counting problems. The class is inspired in a special kind of non-deterministic Turing machines, called counting Turing machines, introduced by L. Valiant. A polynomial-time and uniform solution to the counting version of the SAT problem (a well-known \(\#\) P-complete problem) is also provided, by using a family of counting polarizationless P systems with active membranes, without dissolution rules and division rules for non-elementary membranes but where only very restrictive cooperation (minimal cooperation and minimal production) in object evolution rules is allowed.

Design Patterns for Efficient Solutions to NP-Complete Problems in Membrane Computing

Many variants of P systems have the ability to generate an exponential number of membranes in linear time. This feature has been exploited to elaborate (theoretical) efficient solutions to \(\mathbf{NP}\)-complete, or even harder, problems. A thorough review of the existent solutions shows the utilization of common techniques and procedures. The abstraction of the latter into design patterns can serve to ease and accelerate the construction of efficient solutions to new hard problems.

Fuzzy reasoning spiking neural P systems revisited: A formalization

Abstract Research interest within membrane computing is becoming increasingly interdisciplinary. In particular, one of the latest applications is fault diagnosis. The underlying mechanism was conceived by bridging spiking neural P systems with fuzzy rule-based reasoning systems. Despite having a number of publications associated with it, this research line still lacks a proper formalization of the foundations.

Sevilla Carpets Revisited: Enriching the Membrane Computing Toolbox

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.