Abstract not found

. Finding a natural meeting ground between the highly developed complexity theory of computer science ---with its historical roots in logic and the discrete mathematics of the integers--- and the traditional domain of real computation, the more eclectic less foundational field of numerical analysis ---with its rich history and longstanding traditions in the continuous mathematics of analysis--- presents a compelling challenge. Here we illustrate the issues and pose our perspective toward resolution. This article is essentially the introduction of a book with the same title (to be published by Springer) to appear shortly. Webster: A public declaration of intentions, motives, or views. k Partially supported by NSF grants. y International Computer Science Institute, 1947 Center St., Berkeley, CA 94704, U.S.A., lblum@icsi.berkeley.edu. Partially supported by the Letts-Villard Chair at Mills College. z Universitat Pompeu Fabra, Balmes 132, Barcelona 08008, SPAIN, cucker@upf.es. P...

Abstract. Formal syntax has hitherto worked mostly with theoretical frameworks that take grammars to be generative, in Emil Post’s sense: they provide recursive enumerations of sets. This work has its origins in Post’s formalization of proof theory. There is an alternative, with roots in the semantic side of logic: model-theoretic syntax (MTS). MTS takes grammars to be sets of statements of which (algebraically idealized) well-formed expressions are models. We clarify the difference between the two kinds of framework and review their separate histories, and then argue that the generative perspective has misled linguists concerning the properties of natural languages. We select two elementary facts about natural language phenomena for discussion: the gradient character of the property of being ungrammatical and the open nature of natural language lexicons. We claim that the MTS perspective on syntactic structure does much better on representing the facts in these two domains. We also examine the arguments linguists give for the infinitude of the class of all expressions in a natural language. These arguments turn out on examination to be either unsound or lacking in empirical content. We claim that infinitude is an unsupportable claim that is also unimportant. What is actually needed is a way of representing the structure of expressions in a natural language without assigning any importance to the notion of a unique set with definite cardinality that contains all and only the expressions in the language. MTS provides that.

1 An understanding of learning -- the process by which a learner acquires and refines a broad range of knowledge and skills -- is central to the enterprise of building truly adaptive, flexible, robust, and creative intelligent systems. Significant theoretical and empirical contributions to the characterization of learning in computational terms have emerged from research in a number of disparate research paradigms. The limitations of individual paradigms and of particular classes of techniques within each paradigm are beginning to be recognized. Converging lines of evidence from multiple sources, both theoretical as well as empirical, suggest that artificial intelligence systems, in order to be able to deal with complex tasks such as recognizing and describing 3-dimensional objects, or communicating in natural language, must be able to effectively utilize a range of learning algorithms operating with an adequate repertoire of representational structures. This paper draws on a broad ran...

An earlier article [25] discusses the proposition that the storage and processing of information in computers and in brains may often be understood as information compression. A subsequent article [15] criticises the computing aspects of [25] and research on the more specific conjecture that all forms of computing and formal reasoning may usefully be understood as information compression. The present article, which is intended to be intelligible without recourse to earlier articles, answers the main points in [15], tries to correct the many inaccuracies and misconceptions in that article, and discusses related issues. Topics which are discussed include: the way theories are or should be developed; the role of evidence in motivating research; apparent shortcomings in the Turing machine concept as a reason for seeking new principles of computing; the apparent conflict between the idea of `computing as compression' and the fact that computers may create redundancy - and how the contradict...

In this paper we briefly introduce a Wide Spectrum Language and its transformation theory and describe a recent success of the theory: a general recursion removal theorem. Recursion removal often forms an important step in the systematic development of an algorithm from a formal specification. We use semantic-preserving transformations to carry out such developments and the theorem proves the correctness of many different classes of recursion removal. This theorem includes as special cases the two techniques discussed by Knuth [13] and Bird [7]. We describe some applications of the theorem to cascade recursion, binary cascade recursion, Gray codes, and an inverse engineering problem.

This paper concerns the formal study on the generative powers of extended splicing

We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series - the semilinear and the bounded series - both natural generalizations of the semilinear languages, and we study their behaviour under rational operations, morphisms, Hadamard product, and difference. Turning to commutation on sets of words, we then study the notions of centralizer of a language - the largest set commuting with a language -, of root and of primitive root of a set of words. We answer a question raised by Conway more than thirty years ago - asking whether or not the centralizer of any rational language is rational - in the case of periodic, binary, and ternary sets of words, as well as for rational c-codes, the most general results on this problem. We also prove that any code has a unique primitive root and that two codes commute if and only if they have the same primitive root, thus solving two conjectures of Ratoandromanana, 1989. Moreover, we prove that the commutation with an c-code X can be characterized similarly as in free monoids: a language commutes with X if and only if it is a union of powers of the primitive root of X.

Classifier systems are sub-symbolic or dynamic approaches to machine learning. These systems have been studied rather extensively. In this thesis some theoretical results about the long-term behaviour and the computational abilities of classifier systems are derived. Then some experiments are undertaken. The first experiment entails the implementation of a simple logic function, a multiplexer in a simple classifier system. It is shown that this task can be learned very well. The second task that is taught to the system is a mushroom-classification problem that has been researched with other learning systems. It is shown that this task can be learned. The last problem is the parity problem. First it is shown that this problem does not scale linearly with its number of bits in a straightforward classifier system. An attempt is made to solve it with a multilayer classifier-system, but this is found to be almost impossible. Explanations are given of why this should be the case. Then some ...

ed this by imposing an economic model based on two general principles, conservation of money and strong property rights, that together prevent these misallocations. Second, it appears likely that the representation language used by classiers is not computationally universal, nor even suf- ciently powerful, when one restricts consideration to congurations that are dynamically stable[Bau96, LU99]. We address this representation problem by using a more powerful agent language. Our rst economic model, Hayek1, used simple agents, and because of the dynamic stability problem could only solve large BW problems when given intermediate reward for partial progress[Bau96]. Our last economic model, Hayek3, used agents that compute S-expressions[BD00]. This model of computation was not Turing-complete, and so the system could not produce a program capable of solving arbitrary instances. It did, however, produce systems capable of solving random instances with hundreds of blocks, unscr