Abstract: A myth has arisen concerning Turing's article of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine—a myth that has passed into cogn...

Abstract: The coupling of spatial and temporal symmetry breaking instabilities is studied in a two-variable reaction-diffusion model describing semiconductor transport. A variety of spatiotemporal patterns corresponding to pure Hopf and Turing modes, localized patterns, and mixed Turing-Hopf modes including subharmonic spatiotemporal spiking are found. By organizing the results in a time-scale versus space-scale diagram, and by comparing them with a chemical reaction-diffusion model, it is shown that such behavior is generic for a class of extended nonlinear dynamic systems near codimension-two Turing-Hopf bifurcations.

Abstract: Steady spatial self-organization of three-dimensional chemical reaction-diffusion systems is discussed with the emphasis put on the possible defects that may alter the Turing patterns. It is shown that one of the stable defects of a three-dimensional lamellar Turing structure is a twist grain boundary embedding a Scherk minimal surface.

Abstract: Back in the heyday of computer hardware, some notable people actually believed that sentient computer programs were literally just around the corner. This prompted the great British mathemetician, Alan Turing, to devise a simple test of intelligence. If a computer program could pass the Turing test, then it could be said to be exhibiting intelligence. In 1991, the Cambridge Centre for Behavioural Studies held the first formal instantiation of the Turing Test. In this incarnation the test was known as the Loebner contest, as Dr. Hugh Loebner pledged a $100,000 grand prize for the first computer program to pass the test. I have submitted two computer programs to the 1996 Loebner contest, which is to be held on Friday April 19 in New York city. These computer programs are nothing more than glorious hacks, but in constructing them I have learned a great deal about how language works. In this paper I will describe in detail how my computer programs work, and will make comparisons with similar computer programs such as ELIZA. After this, I will explain why the Loebner contest is doomed to failure.

Abstract: Alan Turing's 1936 paper ON COMPUTABLE NUMBERS, introducing the Turing machine, was a landmark of twentieth century thought. It provided the principle of the post-war electronic computer. Influenced by his crucial codebreaking work in thesecond world war, Turing argued that all the operations of the mind could be performed by computers. His thesis, made famous by the wit and drama of the Turing Test, is the cornerstone of modern Artificial Intelligence. Andrew Hodgesgives a fresh and interesting analysis of Turing's developing thought, relating it to his extraordinary life.

Abstract: Watson-Crick complementarity is one of the very central components of DNA computing, the other central component being the massive parallelism of DNA strands. While the latter component drastically reduces time complexity, the former component is the cause behind the Turing universality of models of DNA computing. This paper makes this cause explicit and also discusses it in terms of some specific models. Finally, another aspect of complementarity, the operational one, will be discussed in terms of Lindenmayer systems.

Abstract: Rice's Theorem says that every nontrivial semantic property of programs is undecidable. It this spirit we show the following: Every nontrivial absolute (gap, relative) counting property of circuits is UP-hard with respect to polynomial-time Turing reductions.

Abstract: The current controversies about mechanism (or computationalism) in Cognitive Science (CS, for short) cannot be properly understood without having a relatively clear idea of what mechanism in CS is. Turing’s thesis (TT, for short) contributes to clarifying the meaning of the expressions ‘mechanistic theory’ and ‘mechanism’. This is the basic view, whose motivations are made explicit in section 2, of the import of TT for the philosophy of CS. In particular, TT enables one to set a necessary condition (hereinafter referred to as Cf) on theories in CS to count as mechanistic. This is a functional condition requiring that the laws accounting for the input/output behavior of the subjects in the domain of the theory be expressible in terms of Turing computable functions.

Abstract: This paper explores Church‘s Thesis and related claims made by Turing. Church‘s Thesis concerns computable numerical functions, while Turing‘s claims concern both procedures for manipulating uninterpreted marks and machines that generate the results that these procedures would yield. It is argued that Turing‘s claims are true, and that they support (the truth of) Church‘s Thesis. It is further argued that the truth of Turing‘s and Church‘s Theses has no interesting consequences for human cognition or cognitive abilities. The Theses don‘t even mean that computers can do as much as people can when it comes to carrying out effective procedures. For carrying out a procedure is a purposive, intentional activity. No actual machine does, or can do, as much.

Abstract: We study the effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems. For this purpose, the Gierer-Meinhardt model of pattern formation is considered. The cases we study are (i) randomness in the underlying lattice structure; (ii) the case in which there is a probability p that at a lattice site both reaction and diffusion occur, otherwise there is only diffusion; and finally, the effect of (iii) anisotropic and (iv) random diffusion coefficients on the formation of Turing patterns. The general conclusion is that the Turing mechanism of pattern formation is fairly robust in the presence of randomness and anisotropy.

Abstract: As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formula Having graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations In the course of time, slide rules were replaced by pocket calculators and personal computers, but I stuck to my original decision My computer phobia did not prevent me from taking an interest in the theoretical question: what is a computation? This question goes back to Hilbert's 10th problem (see Browder [1976]), which asks for an algorithm, or computational procedure, to decide whether any given polynomial equation is solvable in integers It quickly leads to the related question: which numerical functions f : ℕ n → ℕ are computable? While Hilbert's 10th problem was only resolved in 1970, this related question had some earlier answers, of which I shall single out the following three: (1) f is recursive (Godel, Kleene), (2) f is computable on an abstract machine (Turing, Post), (3) f is definable in the untyped λ-calculus (Church, Kleene) These tentative answers were shown to be equivalent by Church [1936] and Turing [1936–7] I shall discuss here some of the more recent developments of these notions of computability and their relevance to linguistics and logic I hope to be forgiven for dwelling on some of the work I have been involved with personally, with greater emphasis than is justified by its historical significance

Abstract: In 1936, when the world was computerless, Alan Turing invented the first virtual machine, now called the Universal Turing Machine (A. Turing, 1936). This concept provided a common ground for a theoretical exploration of the computable. Today, in a world with millions of computers linked to form a global computing network, we are again contemplating the virtues of virtual machines. Will a virtual machine, executing on millions of physical computing devices, be as useful in computing practice as Turing's machine is in computer theory? The author argues that it will and that its coming is inevitable. These considerations pertain to the delivery systems part of the Internet architecture which is presented.

Abstract: In this paper we review the historical development of computer chess and discuss its impact on the concept of intelligence. With the advent of electronic computers after the Second World War, interest in computer chess was stimulated by the seminal papers of Shannon (1950) and Turing (1953). The influential paper of Shannon introduced the classification of chess playing programs into either type A (brute force) or type B (selective). Turing's paper (1953) highlighted the importance of only evaluating 'dead positions' which have no outstanding captures. The brute force search method is the most popular approach to solving the chess problem today. Search enhancements and pruning techniques developed since that era have ensured the continuing popularity of the type A method. Alpha-beta pruning remains a standard technique. Other important developments are surveyed. A popular benchmark test for determining intelligence is the Turing test. In the case of a computer program playing chess the moves are generated algorithmically using rules that have been programmed into the software by a human mind. A key question in the artificial intelligence debate is to what extent computer bytes aided by an arithmetic processing unit can be claimed to 'think'.

Abstract: The present work deals with language learning from text. It considers universal learners for classes of languages in models of additional information and analyzes their complexity in terms of Turing degrees. The following is shown: If the additional information is given by a set containing at least one index for each language from the class to be learned but no index for any language outside the class then there is a universal learner having the same Turing degree as the inclusion problem for enumerable sets. This result is optimal in the sense that any further learner has the same or higher Turing degree. If the additional information is given by a set which contains exactly the indices of the languages from the class to be learned then there is a computable universal learner. Finally, if the additional information is presented as an upper bound on the size of some grammar that generates the language then a high oracle is necessary and sufficient.

Abstract: In 1936, when the world was computerless, Alan Turing invented the first virtual machine, now called the Universal Turing Machine (A. Turing, 1936). This concept provided a common ground for a theoretical exploration of the computable. Today, in a world with millions of computers linked to form a global computing network, we are again contemplating the virtues of virtual machines. Will a virtual machine, executing on millions of physical computing devices, be as useful in computing practice as Turing's machine is in computer theory? The author argues that it will and that its coming is inevitable. These considerations pertain to the delivery systems part of the Internet architecture which is presented.

Abstract: Turing showed the existence of a model universal for the set of Turing machines in the sense that given an encoding of any Turing machine as input the universal Turing machine simulates it. We introduce the concept of universality for reactive systems and construct a CCS process universal in the sense that, given an encoding of any CCS process, it behaves like this process up to weak bisimulation. This construction has a rather non-constructive use of silent actions and we argue that this would be the case for any universal CCS process.

Abstract: It is an irony of history that Alan Turing actually offered the main ingredient for an elegant proof of the non-algorithmic nature of human understanding [1]. Turing has always been convinced that human intellect, though (sometimes) more powerful than computers, is not essentially superior [2], Yet his argument is not very convincing, and does not stand the more recent critique of Roger Penrose [3].

Abstract: T hroughout history, humans have used tools to automate labor-intensive tasks. Employing machines to replace manual labor is commonplace, but automation of cognitive jobs is now also becoming possible. Generally, some form of artificial intelligence is required for a machine to assume cognitive functions. To this end, many artificial intelligence computer languages have been developed that allow users to obtain expert advice on various topics from car mechanics to strategic business planning. These are primarily rule-based languages that evaluate data in a predictable and orderly fashion. These languages have served well for problems in which the parameters and their interrelationships are completely known. Unfortunately, rule-based languages do not lend themselves to tasks, such as interpretation of medical images, that require the integration of visual data with medical knowledge in the absence of explicitly defmed rules. As a result, attempts to apply rule-based artificial intelligence techniques to radiologic image interpretation has generally met with clinically ineffective results [1]. Another type of artificial intelligence, known as artificial neural networks, shows promise toward handling cognitive functions such as pattern recognition and can be applied to medicine and to radiology in particular [2]. Artificial neural networks are so named because they are inspired by, but not necessarily modeled after, biologic neural systems, with which they show some uncanny similarities in behavior. Standard linear computers, present on many desktops, are based on the Turing model. Turing was an early 20th century British mathematician who theorized that all cognitive behavior could be simulated with a ticker-tape with holes punched in sequence to show ones and zeroes. Assuming that the holes are in known positions on the tape in a predefined code, a machine with a counter (or central processing unit) could store and analyze all types of informarion. Turing’s idea appealed to cognitive behaviorists of the day who believed that this machine for information storage and processing represented the way the mind functions. Although Turing’s machine, with a central processing unit and address-relocatable memory, has served as an admirable paradigm for modem computers, no evidence exists that human brains actually function in this manncr. Indeed, a large body of evidence exists to the contrary. For example, human brains do not appear to have any single central processing unit. Tracing cognitive function has been exceedingly difficult, and no investigator to my knowledge has ever been able to locate a single set of neurons that correspond to a discrete memory or set of memories from a particular period of life. In fact, brain ablation studies suggest that human brains store information diffusely through networks that may even contain other, unrelated information. The difference in design between linear computers and artificial neural networks is manifested in the type of problems each is best suited to handle. Linear computers are fabubus for routine numerical manipulations such as addition, subtraction, multiplication, and division and for logic problems (Fig. 1). Networks, on the other hand, are not. Their entire construction is designed for pattern recognition via integration of information. This is much like a human brain. Although most of us are not proficient at manipulating even moderate numbers in our heads, we are capable of recognizing patterns quickly (Fig. 2). In addition, although linear computers must handle information one piece at a time, neural networks-just like humans-integrate information. When posed with a complex decision, such as whether to buy the red or the black sports car, humans do not individually scrutinize each factor involved in making the dccision but rather integrate the information and reach a decision without conscious processing. An example may help to explain how information may be processed and stored in a neural network. Consider 1000 students in a study hall, each with a battery, switch, and ammeter that is calibrated to an arbitrary scale ranging from one to 10. Each student’s

Abstract: In this article we discuss a test described by A M Turing to find out whether a computer program exhibits intelligence and also of its modified versions used to evaluate expert systems and natural language conversations generated by computer programs.

Abstract: The theorems of Kurt Godel and Alan Turing are likely to be remembered as the two most important achievements in mathematics of the twentieth century. Their far-reaching consequences are valid for any formal system and in particular for arithmetic and any advanced mathematical theory. Their formulation in the thirties has changed completely the objectives of the research for the foundations of mathematical theories. The task Hilbert had indicated, namely the reduction of mathematics to logic through the process of axiomatisation and the formulation of a method to answer mechanically any mathematical question, has been proved to be unfeasible.

Abstract: We prove thaf the theory of EXPTIME degrees wzth respect to polynomral fame Turing and many-one reducabdzty a5 undecadablr To do 50 ue use a codzng method based on adeal lattacrs of Boolean algebras whzch was t1,troduced an [Y] The method can be applied zn fact to all hyper-polynomial tame classes

Abstract: Robots have become more and more sophisticated. Every robot has its limits. If we face a task that existing robots cannot solve, then, before we start improving these robots, it is important to check whether it is, in principle, possible to design a robot for this task or not. For that, it is necessary to describe what exactly the robots can, in principle, do. A similar problem - to describe what exactly computers can do - has been solved as early as 1936, by Turing. In this paper, we describe a framework within which we can, hopefully, formalize and answer the question of what exactly robots can do.

Abstract: The uctuation models of self-organization are proposed with uc-tuation Hamiltonians taken into account. Conditions of the Hopf and Turing bifurcations are examined, special attention is paid for the analysis of limit-cycle and focus solutions. The principal possibility of the formation of ordered structures in the uctuation models of self-organization are discussed for open systems in a stationary states.

Abstract: The paper presents the heuristics and techniques which are used to implement automated natural deduction prover (ANDP), the natural deduction was adapted from Gentzen system. There are 4 rules for quantifiers in Gentzen system and we have two unification algorithms in the system ANDP to handle quantifiers. Andrews' Challenge and Turing Halting Problem were solved using ANDP.