by Tien D. Kieu, H. A. Buchdahl – arxiv.org/quant-ph/0504101. 2005

“. Abstract. We give an overview of a quantum adiabatic algorithm for Hilbert’s tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diopha. “

Abstract. We give an overview of a quantum adiabatic algorithm for Hilbert’s tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diophantine equations are presented. We also discuss some prejudicial misunderstandings as well as some plausible difficulties faced by the algorithm in its physical implementations. “To believe otherwise is merely to cling to a prejudice which only gives rise to further prejudices. ” 1

y Turing for the non-existence of a Turing computable halting function. Unfortunately, some have used these arguments to rule out any kind of hypercomputation beyond the capability of Turing machines =-=[13]-=-! We have considered carefully the implicit assumptions of Cantor’s diagonal arguments and pointed out elsewhere [41] (see also [53]) the fallacies of such misuse of Cantor’s diagonlisation. In partic.

by Gualtiero Piccinini

“. This paper offers an account of what it is for a physical system to be a computing mechanism—a system that performs computations. A computing mechanism is a mechanism whose function is to generate output strings from input strings and (possibly) internal states, in accordance with a general rule tha. “

This paper offers an account of what it is for a physical system to be a computing mechanism—a system that performs computations.

A computing mechanism is a mechanism whose function is to generate output strings from input strings and (possibly) internal states, in accordance with a general rule that applies to all relevant strings and depends on the input strings and (possibly) internal states for its application. This account is motivated by reasons endogenous to the philosophy of computing, namely, doing justice to the practices of computer scientists and computability theorists. It is also an application of recent literature on mechanisms, because it assimilates computational explanation to mechanistic explanation. The account can be used to individuate computing mechanisms and the functions they compute and to taxonomize computing mechanisms based on their computing power. 1. Introduction. This

putable are theCOMPUTING MECHANISMS 519 recursive ones. There is an ongoing controversy over the physical possibility of hypercomputers—mechanisms that compute nonrecursive functions (Copeland 2002; =-=Cotogno 2003-=-). I do not have room to address the hypercomputation controversy here. But that controversy should not be resolved by stipulating that hypercomputers do not perform computations. A good account of co.

by Gualtiero Piccinini – Philosophy of Science. Piccinini, G. (forthcoming b). “Computation without Representation,” Philosophical. 2007

“. According to pancomputationalism, everything is a computing system.

In this paper, I distinguish between different varieties of pancomputationalism. I find that although some varieties are more plausible than others, only the strongest variety is relevant to the philosophy of mind, but only the most. “

According to pancomputationalism, everything is a computing system. In this paper, I distinguish between different varieties of pancomputationalism. I find that although some varieties are more plausible than others, only the strongest variety is relevant to the philosophy of mind, but only the most trivial varieties are true. As a side effect of this exercise, I offer a clarified distinction between computational modelling and computational explanation. I. Pancomputationalism and the Computational Theory of Mind The main target of this paper is pancomputationalism, according to which everything is a computing system. I have encountered two peculiar responses to pancomputationalism: some philosophers find it obviously false, too silly to be worth refuting; others find it obviously true, too trivial to require a defence. Neither camp sees the need for this paper. But neither camp seems aware of the other camp. The existence of both camps, together with continuing appeals to pancomputationalism in the literature, compel me to analyse the matter more closely. In this paper, I distinguish between different varieties of pancomputationalism. I find that although some are more plausible than others, only the strongest variety is relevant to the philosophy of mind, but only the most trivial varieties are true. As a side effect of this exercise, I offer a clarified distinction between computational modelling and computational explanation. The canonical formulation of pancomputationalism is due to Hilary Putnam: ‘everything is a Probabilistic Automaton under some Description’ [Putnam 1999: 31; ‘probabilistic automaton ’ is Putnam’s term for

by Petrus H. Potgieter – Theoretical Computer Science

“. 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 straightforward option: Zeno machines (Turing machines with accelerating clock). The halting problem is br. “

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 straightforward 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 suggested that claims to have “broken the Turing barrier ” could be toned down and that the important and well-founded rôle of Turing computability in the mathematical sciences stands unchallenged.

ls us the mathematical constraints on what can be computed given the way we have defined computing. which this subsection has attempted to illustrate. A similar exposition can be found in [17] and in =-=[26]-=-. Ord and Kieu [27] have examined the halting problem in a similar context and although they do not disagree with the premises or with the conclusion, they do not find it an argument detracting from t.

by GUALTIERO PICCININI. 2007

“. The Church–Turing Thesis (CTT) is often employed in arguments for computationalism. I scrutinize the most prominent of such arguments in light of recent work on CTT and argue that they are unsound. Although CTT does nothing to support computationalism, it is not irrelevant to it. By eliminating mis. “

The Church–Turing Thesis (CTT) is often employed in arguments for computationalism. I scrutinize the most prominent of such arguments in light of recent work on CTT and argue that they are unsound. Although CTT does nothing to support computationalism, it is not irrelevant to it. By eliminating misunderstandings about the relationship between CTT and computationalism, we deepen our appreciation of computationalism as an empirical hypothesis.

by Apostolos Syropoulos. 2003

“. Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multi-fuzzy set (i.e. multisets. “

Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multi-fuzzy set (i.e. multisets where objects are repeated to some degree), we introduce two variants of P systems with fuzzy components: P systems with fuzzy data and P systems with fuzzy multiset rewriting rules. By silently assuming that fuzzy data are not the result of some fuzzification process, P systems with fuzzy data are shown to be a step towards real hypercomputation.

by Gualtiero Piccinini

Abstract not found

by Peter Kugel – Theoretical Computer Science

“. In 1950, Turing suggested that intelligent behavior might require “a departure from the completely disciplined behaviour involved in computation”, but nothing that a digital computer could not do. In this paper, I want to explore Turing’s suggestion by asking what it is, beyond computation, that int. “

In 1950, Turing suggested that intelligent behavior might require “a departure from the completely disciplined behaviour involved in computation”, but nothing that a digital computer could not do. In this paper, I want to explore Turing’s suggestion by asking what it is, beyond computation, that intelligence might require, why it might require it and what knowing the answers to the first two questions might do to help us understand artificial and natural intelligence.

by Antony Van, Der Mude

“. Abstract. Contemporary mathematicians since the time of Frege have hypothesized that the objects of mathematics exist in a Platonic universe. Mathematical Platonism is part of the Doctrine of the Forms, which was criticized by Aristotle, who stated that the Forms do not exist apart from the things o. “

Abstract. Contemporary mathematicians since the time of Frege have hypothesized that the objects of mathematics exist in a Platonic universe. Mathematical Platonism is part of the Doctrine of the Forms, which was criticized by Aristotle, who stated that the Forms do not exist apart from the things of the real world- a theory known as Hylomorphism. This paper postulates that the observer in the Copenhagen Interpretation of Quantum Mechanics can be represented as a hylomorphic function. These functions, since they compute universal properties of real events, are not time invertible, like most theories of physics. Instead, they define the arrow of time and the information carried by physical media. They also represent the atomic Qualia of subjective experience. Since Church’s thesis seems to be a universal property of reality, the effective procedures seem to be an underlying representation of hylomorphic functions over the integers. But due to quantum undecidability, the hylomorphic functions are not effective, but hypercomputations that cannot be computed by a finite procedure. An example of a hypercomputation is the task of Learning in the Limit (similar to Identification in the Limit) over recursively enumerable sets of inputs. The Kolmogorov set of incompressible numbers is an example of this class of functions- but they are random numbers. On the other hand, although reality has a random component, it is predictable within that randomness. We illustrate a hypercomputation that is Learnable in the Limit, such that there is a computable function that gets arbitrarily close in accuracy to this hypercomputation. It is an example of how hylomorphic functions can model physical observations. This implies that though there can be no axiomatic Theory of Everything, we can come up with theories that are more and more accurate the more we learn. 1.

just to the effective procedures. The hylomorphic functions can be composed of primitive or general recursive functions, but not be effective. Functions such as these are known as hypercomputation[16]=-=[5]-=- or supertasks. For example, the first two levels of the Arithmetic Hierarchy are the primitive recursive and general recursive functions, but the higher levels of the hierarchy are not effectively co.

by Vincent C. Müller – FORTHCOMING IN MINDS AND MACHINES. 2011

“. This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses prop. “

This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with “Zeno-machines”, i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though noneffective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation.