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The many forms of hypercomputation
 Applied Mathematics and Computation
, 2006
"... This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess. ..."
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This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess.
BioSteps Beyond Turing
 BIOSYSTEMS
, 2004
"... Are there `biologically computing agents' capable to compute Turing uncomputable functions? It is perhaps tempting to dismiss this question with a negative answer. Quite the opposite, for the first time in the literature on molecular computing we contend that the answer is not theoretically nega ..."
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Are there `biologically computing agents' capable to compute Turing uncomputable functions? It is perhaps tempting to dismiss this question with a negative answer. Quite the opposite, for the first time in the literature on molecular computing we contend that the answer is not theoretically negative. Our results will be formulated in the language of membrane computing (P systems). Some mathematical results presented here are interesting in themselves. In contrast with most speedup methods which are based on nondeterminism, our results rest upon some universality results proved for deterministic P systems. These results will be used for building "accelerated P systems". In contrast with the case of Turing machines, acceleration is a part of the hardware (not a quality of the environment) and it is realised either by decreasing the size of "reactors" or by speedingup the communication channels.
Logic and Complexity in Cognitive Science
, 2011
"... How can logic help us to understand cognition? One answer is provided by the computational perspective, which treats cognition as information flow in a computational system. This perspective draws an analogy between intelligent behavior as we observe it in human beings and the complex behavior ..."
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How can logic help us to understand cognition? One answer is provided by the computational perspective, which treats cognition as information flow in a computational system. This perspective draws an analogy between intelligent behavior as we observe it in human beings and the complex behavior
A Hierarchical Classification of FirstOrder Recurrent Neural Networks
 4TH INTERNATIONAL CONFERENCE ON LANGUAGE AND AUTOMATA THEORY AND APPLICATIONS, TRIER: GERMANY
, 2011
"... We provide a refined hierarchical classification of firstorder recurrent neural networks made up of McCulloch and Pitts cells. The classification is achieved by first proving the equivalence between the expressive powers of such neural networks and Muller automata, and then translating the Wadge cl ..."
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We provide a refined hierarchical classification of firstorder recurrent neural networks made up of McCulloch and Pitts cells. The classification is achieved by first proving the equivalence between the expressive powers of such neural networks and Muller automata, and then translating the Wadge classification theory from the automatatheoretic to the neural network context. The obtained hierarchical classification of neural networks consists of a decidable prewell ordering of width 2 and height ω ω, and a decidability procedure of this hierarchy is provided. Notably, this classification is shown to be intimately related to the attractive properties of the networks, and hence provides a new refined measurement of the computational power of these networks in terms of their attractive behaviours.
Neural computation and the computational theory of cognition. Cognitive science
, 2012
"... We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computati ..."
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We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism—neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous signals; digital computation requires strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike trains, are graded like continuous signals but are constituted by discrete functional elements (spikes); thus, typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. Finally, we highlight three important consequences of a proper understanding of neural computation for the theory of cognition. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on nonneural notions of computation ought to be replaced or reinterpreted in terms of neural computation.
Misbehaving Machines: The Emulated Brains of Transhumanist Dreams
"... Enhancement technologies may someday grant us capacities far beyond what we now consider humanly possible. Nick Bostrom and Anders Sandberg suggest that we might survive the deaths of our physical bodies by living as computer emulations. In 2008, they issued a report, or “roadmap, ” from a conferenc ..."
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Enhancement technologies may someday grant us capacities far beyond what we now consider humanly possible. Nick Bostrom and Anders Sandberg suggest that we might survive the deaths of our physical bodies by living as computer emulations. In 2008, they issued a report, or “roadmap, ” from a conference where experts in all relevant fields collaborated to determine the path to “whole brain emulation. ” Advancing this technology could also aid philosophical research. Their “roadmap ” defends certain philosophical assumptions required for this technology‟s success, so by determining the reasons why it succeeds or fails, we can obtain empirical data for philosophical debates regarding our mind and selfhood. The scope ranges widely, so I merely survey some possibilities, namely, I argue that this technology could help us determine (1) if the mind is an emergent phenomenon, (2) if analog technology is necessary for brain emulation, and (3) if neural randomness is so wild that a complete emulation is impossible.
The Expressive Power of Analog Recurrent Neural Networks on Infinite Input Streams
, 2012
"... We consider analog recurrent neural networks working on infinite input streams, provide a complete topological characterization of their expressive power, and compare it to the expressive power of classical infinite word reading abstract machines. More precisely, we consider analog recurrent neural ..."
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We consider analog recurrent neural networks working on infinite input streams, provide a complete topological characterization of their expressive power, and compare it to the expressive power of classical infinite word reading abstract machines. More precisely, we consider analog recurrent neural networks as language recognizers over the Cantor space, and prove that the classes of ωlanguages recognized by deterministic and nondeterministic analog networks correspond precisely to the respective classes of Π 0 2sets and Σ 1 1sets of the Cantor space. Furthermore, we show that the result can be generalized to more expressive analog networks equipped with any kind of Borel accepting condition. Therefore, in the deterministic case, the expressive power of analog neural nets turns out to be comparable to the expressive power of any kind of Büchi abstract machine, whereas in the nondeterministic case, analog recurrent networks turn out to machine, including the main cases of classical automata, 1counter automata, kcounter automata, pushdown automata, and Turing machines.
Chapter Nine
"... This is a preprint of an article whose final and definitive form will be published in ..."
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This is a preprint of an article whose final and definitive form will be published in