Propositional computability logic I

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of "always computable" problems. The present contribution gives a detailed exposition of a soundness and completeness proof for an axiomatization of one of the most basic fragments of computability logic. The logical vocabulary of this fragment contains operators for the so called parallel and choice operations, and its atoms represent elementary problems, i.e. predicates in the standard sense. This article is self-contained as it explains all relevant concepts. While not technically necessary, however, familiarity with the foundational paper "Introduction to computability logic" [Annals of Pure and Applied Logic 123 (2003), pp.1-99] would greatly help the reader in understanding the philosophy, underlying motivations, potential and utility of computability logic, -- the context that determines the value of the present results. Online introduction to the subject is available at http://www.cis.upenn.edu/~giorgi/cl.html and http://www.csc.villanova.edu/~japaridz/CL/gsoll.html .Comment: To appear in ACM Transactions on Computational Logi

Multiple Particle Interference and Quantum Error Correction

The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer. Methods of error correction in the quantum regime are presented, and their limitations assessed. A quantum channel can recover from arbitrary decoherence of x qubits if K bits of quantum information are encoded using n quantum bits, where K/n can be greater than 1-2 H(2x/n), but must be less than 1 - 2 H(x/n). This implies exponential reduction of decoherence with only a polynomial increase in the computing resources required. Therefore quantum computation can be made free of errors in the presence of physically realistic levels of decoherence. The methods also allow isolation of quantum communication from noise and evesdropping (quantum privacy amplification).Comment: Submitted to Proc. Roy. Soc. Lond. A. in November 1995, accepted May 1996. 39 pages, 6 figures. This is now the final version. The changes are some added references, changed final figure, and a more precise use of the word `decoherence'. I would like to propose the word `defection' for a general unknown error of a single qubit (rotation and/or entanglement). It is useful because it captures the nature of the error process, and has a verb form `to defect'. Random unitary changes (rotations) of a qubit are caused by defects in the quantum computer; to entangle randomly with the environment is to form a treacherous alliance with an enemy of successful quantu

Are there new models of computation? Reply to Wegner and Eberbach

Wegner and Eberbach[Weg04b] have argued that there are fundamental limitations to Turing Machines as a foundation of computability and that these can be overcome by so-called superTuring models such as interaction machines, the [pi]calculus and the $-calculus. In this paper we contest Weger and Eberbach claims

Light driven structuring of glasses

Theoretical and experimental evidence of light driven structuring of glasses is presented. We show that light overcomes Coulomb repulsion and effective electron-electron interaction in glasses under strong light pumping becomes attractive. As the result homogenious distribution of trapped electrons gets unstable and macroscopic electron bunches are grown. At different conditions ordered structures with period about 2 microns determined by internal properties of the material are formed These structures were observed in ablation: surface profile after laser treatment reveals ordered pattern corresponding to the light induced electron domains.Comment: 7 pages, 6 figure

Learning, Social Intelligence and the Turing Test - why an "out-of-the-box" Turing Machine will not pass the Turing Test

The Turing Test (TT) checks for human intelligence, rather than any putative general intelligence. It involves repeated interaction requiring learning in the form of adaption to the human conversation partner. It is a macro-level post-hoc test in contrast to the definition of a Turing Machine (TM), which is a prior micro-level definition. This raises the question of whether learning is just another computational process, i.e. can be implemented as a TM. Here we argue that learning or adaption is fundamentally different from computation, though it does involve processes that can be seen as computations. To illustrate this difference we compare (a) designing a TM and (b) learning a TM, defining them for the purpose of the argument. We show that there is a well-defined sequence of problems which are not effectively designable but are learnable, in the form of the bounded halting problem. Some characteristics of human intelligence are reviewed including it's: interactive nature, learning abilities, imitative tendencies, linguistic ability and context-dependency. A story that explains some of these is the Social Intelligence Hypothesis. If this is broadly correct, this points to the necessity of a considerable period of acculturation (social learning in context) if an artificial intelligence is to pass the TT. Whilst it is always possible to 'compile' the results of learning into a TM, this would not be a designed TM and would not be able to continually adapt (pass future TTs). We conclude three things, namely that: a purely "designed" TM will never pass the TT; that there is no such thing as a general intelligence since it necessary involves learning; and that learning/adaption and computation should be clearly distinguished.Comment: 10 pages, invited talk at Turing Centenary Conference CiE 2012, special session on "The Turing Test and Thinking Machines

Turing's three philosophical lessons and the philosophy of information

In this article, I outline the three main philosophical lessons that we may learn from Turing's work, and how they lead to a new philosophy of information. After a brief introduction, I discuss his work on the method of levels of abstraction (LoA), and his insistence that questions could be meaningfully asked only by specifying the correct LoA. I then look at his second lesson, about the sort of philosophical questions that seem to be most pressing today. Finally, I focus on the third lesson, concerning the new philosophical anthropology that owes so much to Turing's work. I then show how the lessons are learned by the philosophy of information. In the conclusion, I draw a general synthesis of the points made, in view of the development of the philosophy of information itself as a continuation of Turing's work. This journal is © 2012 The Royal Society.Peer reviewe

An evolutionary model with Turing machines

The development of a large non-coding fraction in eukaryotic DNA and the phenomenon of the code-bloat in the field of evolutionary computations show a striking similarity. This seems to suggest that (in the presence of mechanisms of code growth) the evolution of a complex code can't be attained without maintaining a large inactive fraction. To test this hypothesis we performed computer simulations of an evolutionary toy model for Turing machines, studying the relations among fitness and coding/non-coding ratio while varying mutation and code growth rates. The results suggest that, in our model, having a large reservoir of non-coding states constitutes a great (long term) evolutionary advantage.Comment: 16 pages, 7 figure

Can Machines Think in Radio Language?

People can think in auditory, visual and tactile forms of language, so can machines principally. But is it possible for them to think in radio language? According to a first principle presented for general intelligence, i.e. the principle of language's relativity, the answer may give an exceptional solution for robot astronauts to talk with each other in space exploration.Comment: 4 pages, 1 figur

Examples of Artificial Perceptions in Optical Character Recognition and Iris Recognition

This paper assumes the hypothesis that human learning is perception based, and consequently, the learning process and perceptions should not be represented and investigated independently or modeled in different simulation spaces. In order to keep the analogy between the artificial and human learning, the former is assumed here as being based on the artificial perception. Hence, instead of choosing to apply or develop a Computational Theory of (human) Perceptions, we choose to mirror the human perceptions in a numeric (computational) space as artificial perceptions and to analyze the interdependence between artificial learning and artificial perception in the same numeric space, using one of the simplest tools of Artificial Intelligence and Soft Computing, namely the perceptrons. As practical applications, we choose to work around two examples: Optical Character Recognition and Iris Recognition. In both cases a simple Turing test shows that artificial perceptions of the difference between two characters and between two irides are fuzzy, whereas the corresponding human perceptions are, in fact, crisp.Comment: 5th Int. Conf. on Soft Computing and Applications (Szeged, HU), 22-24 Aug 201

Boundary-driven instability

We analyse a reaction-diffusion system and show that complex spatial patterns can be generated by imposing Dirichlet boundary conditions on one or more of the reactant concentrations. This pattern persists even when the homogeneous steady state with Neumann conditions is stable