Membrane Computing Schema Based on String Insertions

In this note we introduce the notion of a membrane computing schema for string objects. We propose a computing schema for a membrane network (i.e., tissue-like membrane system) where each membrane performs unique type of operations at a time and sends the result to others connected through the channel. The distinguished features of the computing models obtained from the schema are: 1. only context-free insertion operations are used for string generation, 2. some membranes assume ltering functions for structured objects(molecules), 3. the generating model and accepting model are obtained in the same schema, and both are computationally universal, 4. several known rewriting systems with universal computability can be reformulated in terms of membrane computing schema in a uniform manner. The rst feature provides the model with a simple uniform structure which facilitates a biological implementation of the model, while the second feature suggests further feasibility of the model in terms of DNA complementarity. Through the third and fourth features, one may have a uni ed view of a variety of existing rewriting systems with Turing computability in the framework of membrane computing paradigm

Membrane Computing Schema: A New Approach to Computation Using String Insertions

In this paper, we introduce the notion of a membrane computing schema for string objects. We propose a computing schema for a membrane network (i.e., tissue-like membrane system) where each membrane performs unique type of operations at a time and sends the result to others connected through the channel. The distinguished features of the computing models obtained from the schema are: 1. only context-free insertion operations are used for string generation, 2. some membranes assume filtering functions for structured objects (molecules), 3. generating model and accepting model are obtained in the same schema, and both are computationally universal, 4. several known rewriting systems with universal computability can be reformulated by the membrane computing schema in a uniform manner. The first feature provides the model with a simple uniform structure which facilitates a biological implementation of the model, while the second feature suggests further feasibility of the model in terms of DNA complementarity. Through the third and fourth features, one may have a unified view of a variety of existing rewriting systems with Turing computability in the framework of membrane computing paradigm.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

Zeno machines and hypercomputation

This paper reviews the Church-Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of "hypercomputation", concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with accelerating clock). The halting problem is briefly discussed in a general context and the suggestion that it is an inevitable companion of any reasonable computational model is emphasised. It is hinted that claims to have "broken the Turing barrier" could be toned down and that the important and well-founded role of Turing computability in the mathematical sciences stands unchallenged.Comment: 11 pages. First submitted in December 2004, substantially revised in July and in November 2005. To appear in Theoretical Computer Scienc

On the possible Computational Power of the Human Mind

The aim of this paper is to address the question: Can an artificial neural network (ANN) model be used as a possible characterization of the power of the human mind? We will discuss what might be the relationship between such a model and its natural counterpart. A possible characterization of the different power capabilities of the mind is suggested in terms of the information contained (in its computational complexity) or achievable by it. Such characterization takes advantage of recent results based on natural neural networks (NNN) and the computational power of arbitrary artificial neural networks (ANN). The possible acceptance of neural networks as the model of the human mind's operation makes the aforementioned quite relevant.Comment: Complexity, Science and Society Conference, 2005, University of Liverpool, UK. 23 page

On the relevance of the neurobiological analogue of the finite-state architecture

We present two simple arguments for the potential relevance of a neurobiological analogue of the finite-state architecture. The first assumes the classical cognitive framework, is well-known, and is based on the assumption that the brain is finite with respect to its memory organization. The second is formulated within a general dynamical systems framework and is based on the assumption that the brain sustains some level of noise and/or does not utilize infinite precision processing. We briefly review the classical cognitive framework based on Church-Turing computability and non-classical approaches based on analog processing in dynamical systems. We conclude that the dynamical neurobiological analogue of the finite-state architecture appears to be relevant, at least at an implementational level, for cognitive brain systems

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature