Computing with Membranes

Introduction to Geometry. By H. S. M. Coxeter. Pp. xiv, 443. 1961. (John Wiley)

From the Publisher:
This book investigates two major systems: firstly, cooperating distributed grammar systems, where the grammars work on one common sequential form and the cooperation is realized by the control of the sequence of active grammars; secondly, parallel communicating grammar systems, where each grammar works on its own sequential form and cooperation is done by means of communicating between grammars. The investigation concerns hierarchies with respect to different variants of cooperation, relations with classical formal language theory, syntactic parameters such as the number of components and their size, power of synchronization, and general notions generated from artificial intelligence.

Grammar Systems: A Grammatical Approach to Distribution and Cooperation

http://profs.scienze.univr.it/~manca/mnc/membrane.pdf

A guide to membrane computing

P systems are parallel Molecular Computing models based on processing multisets of objects in cell-like membrane structures. Various variants were already shown to be computationally universal, equal in power to Turing machines. In this paper one proposes a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects. Moreover, the membranes can multiply themselves by division. We prove that this variant is not only computationally universal, but also able to solve NP complete problems in polynomial (actually, linear) time. We exemplify this assertion with the well-known SAT problem.

P systems with active membranes: attacking NP-complete problems

Developments in Language Theory II

Grammar systems

On cooperating/distributed grammar systems

We continue the investigation of the power of the computability models introduced in [Gh. Paun, Computing with membranes, TUCS Report 208, November 1998] under the name of transition super-cell systems. We compare these systems with classic mechanisms in formal language theory, context-free and matrix grammars, E0L and ET0L systems, interpreted as generating mechanisms of number relations (we take the Parikh image of the usual language generated by these mechanisms rather than the language). Several open problems are also formulated.

On the Power of Membrane Computing

In [13], N. Chomsky says that “the main problem of immediate relevance to the theory of language is that of determining where in the hierarchy of devices the grammars of natural languages lie.” Formulated in other terms, the question is “where are the natural languages placed in the Chomsky hierarchy?” The debate started in 1959 and is not yet settled. Various arguments over English [4], Mohawk [92], Swiss German [112], Bambara [16], Chinese [95], etc., were given, refuted, rehabilitated — see pro and con arguments as well as further bibliographical information in [38] and [70]. The main difficulty is not a mathematical one but a linguistic one: what is English, what is a natural language, can we separate the syntax and the morphology from semantics or pragmatics? Whatever is or will be the position with respect to these questions, the linguists seem to agree (see again [70]) that “all” natural languages contain constructions which cannot be described by context-free grammars. Three basic such features of natural languages are: 


reduplication, leading to languages of the form {xx | x ∈ V*}


multiple agreements, modeled by languages of the form {a n b n c n | n ≥ 1}, {a n b n c n d n | n ≥ 1}, etc.


crossed agreements, as modeled by {a n b m c n d m | n, m ≥ 1}.

Jürgen Dassow

Papers

Developments in Language Theory II

Grammar systems

On cooperating/distributed grammar systems

On the Power of Membrane Computing

Grammars with controlled derivations