2,399 research outputs found
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
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
Information Processing, Computation and Cognition
Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both â although others disagree vehemently. Yet different cognitive scientists use âcomputationâ and âinformation processingâ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are the same thing. In this paper, we address this unsatisfactory state of affairs by presenting a general and theory-neutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism/computational neuroscience on the other. We defend the relevance to cognitive science of both computation, at least in a generic sense, and information processing, in three important senses of the term. Our account advances several foundational debates in cognitive science by untangling some of their conceptual knots in a theory-neutral way. By leveling the playing field, we pave the way for the future resolution of the debatesâ empirical aspects
Computation vs. Information Processing: Why Their Difference Matters to Cognitive Science
Since the cognitive revolution, itâs become commonplace that cognition involves both computation and information processing. Is this one claim or two? Is computation the same as information processing? The two terms are often used interchangeably, but this usage masks important differences. In this paper, we distinguish information processing from computation and examine some of their mutual relations, shedding light on the role each can play in a theory of cognition. We recommend that theorists of cognition be explicit and careful in choosing\ud
notions of computation and information and connecting them together. Much confusion can be avoided by doing so
Notes on the Mathematical Foundations of Analogue Computation
Digital computing has its mathematical foundations in (classical) recursion theory and constructive mathematics. The implicit, working, assumption of those who practice the noble art of analog computing may well be that the mathematical foundations of their subject is as sound as the foundations of the real analysis. That, in turn, implies a reliance on the soundness of set theory plus the axiom of choice. This is, surely, seriously disturbing from a computation point of view. Therefore, in this paper, I seek to locate a foundation for analog computing in exhibiting some tentative dualities with results that are analogous to those that are standard in computability theory. The main question, from the point of view of economics, is whether the Phillips Machine, as an analog computer, has universal computing properties. The conjectured answer is in the negative.
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