This is a comprehensive (and friendly) introduction to membrane computing (MC), meant to offer both computer scientists and non-computer scientists an up-to-date overview of the field. That is why the set of notions introduced here is rather large, but the presentation is informal, without proofs and with rigorous definitions given only for the basic types of P systems — symbol object P systems with multiset rewriting rules, systems with symport/antiport rules, systems with string objects, tissue-like P systems, and neural-like P systems. Besides a list of (biologically inspired or mathematically motivated) ingredients/features which can be used in systems of these types, we also mention a series of results, as well as a series of research trends and topics.

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Introduction to Membrane Computing

From the Publisher:
This mathematically oriented introduction to the theory of logic programming presents a systematic exposition of the resolution method for propositional, first-order, and Horn- clause logics, together with an analysis of the semantic aspects of the method. It is through the inference rule of resolution that both proofs and computations can be manipulated on computers, and this book contains elegant versions and proofs of the fundamental theorems and lemmas in the proof theory of logic programming. Advanced topics such as recursive complexity and negation as failure and its semantics are covered, and streamlined setups for SLD- and SLDNF-resolution are described.
No other book treats this material in such detail and with such sophistication. Doets provides a novel approach to resolution that is applied to the first-order case and the case of (positive) logic programs. In contrast to the usual approach, the concept of a resolvent is defined nonconstructively, without recourse to the concept of unification, allowing the soundness and completeness proofs to be carried out in a more economic way. Other new material includes computability results dealing with analytical hierarchy, results on infinite derivations and an exposition on general logic programs using 3-valued logic.

From Logic to Logic Programming

The internal organization and functioning of living cells, as well as their cooperation in tissues and higher order structures, can be a rich source of inspiration for computer science, not fully exploited at the present date. Membrane computing is an answer to this challenge, well developed at the theoretical (mathematical and computability theory) level, already having several applications (via usual computers), but without having yet a bio-lab implementation. After briefly discussing some general issues related to natural computing, this paper provides an informal introduction to membrane computing, focused on the main ideas, the main classes of results and of applications. Then, three recent achievements, of three different types, are briefly presented, with emphasis on the usefulness of membrane computing as a framework for devising models of interest for biological and medical research.

https://www.gcn.us.es/files/Biosystems.pdf

Membrane computing: Brief introduction, recent results and applications

This work is a continuation of the investigations aiming to bridge membrane computing (where in a compartmental cell-like structure the chemicals to evolve are placed in the compartments defined by the membranes) and brane calculi (where one considers again a compartmental cell-like structure with the chemicals/proteins placed on the membranes themselves). In the current paper we use objects both in compartments and on membranes (the latter are called proteins), with the objects from membranes evolving under the control of the proteins. Several possibilities are considered (objects only moved across membranes or also changed during this operation, with the proteins only assisting the move/change or also changing themselves). Somewhat expected, computational universality is obtained for several combinations of such possibilities.

P Systems with Proteins on Membranes

We first give a historical overview of the most important results obtained in the area of P systems and tissue P systems with symport/antiport rules, especially with respect to the development of computational completeness results improving descriptional complexity parameters. We consider the number of membranes (cells in tissue P systems), the weight of the rules, and the number of objects. Then we establish our newest results: P systems with only one membrane, symport rules of weight three, and with only seven additional objects remaining in the skin membrane at the end of a halting computation are computationally complete; P systems with minimal cooperation, i.e., P systems with symport/antiport rules of size one and P systems with symport rules of weight two, are computationally complete with only two membranes with only three and six, respectively, superfluous objects remaining in the output membrane at the end of a halting computation.

Computational power of symport/antiport : History, advances, and open problems

We prove that two classes of communicative P systems with 3 membranes and with minimal cooperation, namely P systems with symport/antiport rules of size 1 and and P systems with symport rules of size 2, are computationally complete: they generate all recursively enumerable sets of vectors of nonnegative integers. The result of computation is obtained in the elementary membrane.

Communicative p systems with minimal cooperation

A hybrid network of evolutionary processors (HNEP) is a graph where each node is associated with a special rewriting system called an evolutionary processor, an input filter, and an output filter. Each evolutionary processor is given a finite set of one type of point mutations (insertion, deletion or a substitution of a symbol) which can be applied to certain positions in a string. An HNEP rewrites the strings in the nodes and then re-distributes them according to a filter-based communication protocol; the filters are defined by certain variants of random-context conditions. HNEPs can be considered both as languages generating devices (GHNEPs) and language accepting devices (AHNEPs); most previous approaches treated the accepting and generating cases separately. For both cases, in this paper we show that five nodes are sufficient to accept (AHNEPs) or generate (GHNEPs) any recursively enumerable language by showing the more general result that any partial recursive relation can be computed by an HNEP with (at most) five nodes with the underlying graph structure for the communication between the evolutionary processors being the complete or the linear graph with five nodes, whereas with a star-like communication graph we need six nodes. If the final results are defined by only taking the terminal strings out of the designated output node, then for these extended HNEPs we can prove that only four nodes are needed in all cases--for computing any partial recursive relation as well as for generating and accepting any recursively enumerable language--and the underlying communication structure can be a complete or a linear graph, but now even a star-like graph, too.

Computational completeness of complete, star-like, and linear hybrid networks of evolutionary processors with a small number of processors

In computational processes based on backwards chaining, a rule of the type A ← B1, . . . , Bn is seen as a procedure which points that the problem A can be split into the problems B1, . . . , Bn. In classical devices, the subproblems B1, . . . , Bn are solved sequentially. In this paper we present some questions that circulated during the Second Brainstorming Week related to the application of the parallelism of P systems to computation based on backwards chaining, and we illustrate them with the example of inferential deductive process.

Vladimir Rogozhin

Papers

Communicative p systems with minimal cooperation

Computational completeness of complete, star-like, and linear hybrid networks of evolutionary processors with a small number of processors

Deductive databases and P systems