Abstract. We define the main factor of intelligence as the ability to comprehend, formalising this ability with the help of new constructs based on descriptional complexity. The result is a comprehension test, or C-test, exclusively defined in terms of universal descriptional machines (e.g universal Turing machines). Despite the absolute and non-anthropomorphic character of the test it is equally applicable to both humans and machines. Moreover, it correlates with classical psychometric tests, thus establishing the first firm connection between information theoretic notions and traditional IQ tests. The Turing Test is compared with the C-test and their joint combination is discussed. As a result, the idea of the Turing Test as a practical test of intelligence should be left behind, and substituted by computational and factorial tests of different cognitive abilities, a much more useful approach for artificial intelligence progress and for many other intriguing questions that are presented beyond the Turing Test.

Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like l-calculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] with two remarkable features inherited from its object-oriented coding in C++: it is easily tunable for our needs, and it is efficient. We have made it even more reduced, removing any operand in the instruction set, even for the loop operations. We have only three registers which are AX (the accumulator), BX and CX. The operations Q b we have used for our experiment are in Table 1: LOOPTOP Decrements CX. If it is not equal to the first element jump to the program top.

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This paper is a survey of concepts and results related to simple Kolmogorov complexity, prefix complexity and resource-bounded complexity. We also consider a new type of complexity--- statistical complexity closely related to mathematical statistics. Unlike other discoverers of algorithmic complexity, A. N. Kolmogorov's leading motive was developing on its basis a mathematical theory more adequately substantiating applications of probability theory, mathematical statistics and information theory. Kolmogorov wanted to deduce properties of a random object from its complexity characteristics without use of the notion of probability. In the first part of this paper we present several results in this direction. Though the subsequent development of algorithmic complexity and randomness was different, algorithmic complexity has successful applications in a traditional probabilistic framework. In the second part of the paper we consider applications to the estimation of parameters and the definition of Bernoulli sequences. All considerations have finite combinatorial character. 1.

This paper presents an operative measure of reinforcement for constructive learning methods, i.e., eager learning methods using highly expressible (or universal) representation languages. These evaluation tools allow a further insight in the study of the growth of knowledge, theory revision and abduction. The final approach is based on an apportionment of credit wrt. the ‘course ’ that the evidence makes through the learnt theory. Our measure of reinforcement is shown to be justified by cross-validation and by the connection with other successful evaluation criteria, like the MDL principle. Finally, the relation with the classical view of reinforcement is studied, where the actions of an intelligent system can be rewarded or penalised, and we discuss whether this should affect our distribution of reinforcement. The most important result of this paper is that the way we distribute reinforcement into knowledge results in a rated ontology, instead of a single prior distribution. Therefore, this detailed information can be exploited for guiding the space search of inductive learning algorithms. Likewise, knowledge revision may be done to the part of the theory which is not justified by the

In this paper we develop a computational framework for the measurement of different factors or abilities which are usually found in intelligent behaviours. For this, we first develop a scale for measuring the complexity of an instance of a problem, depending on the descriptional complexity (Levin LT variant) of the ‘explanation ’ of the answer to the problem. We centre on the establishment of either deductive and inductive abilities, and we show that their evaluation settings are special cases of the general framework. Some classical dependencies between them are shown and a way to separate these dependencies is developed. Finally, some variants of the previous factors and other possible ones to be taken into account are investigated. In the end, the application of these measurements for the evaluation of AI progress is discussed.

The classical (Turing) theory of computation has been extraordinarily successful in providing the foundations and framework for theoretical computer science. Yet its dependence on 0s and 1s is fundamentally inadequate for providing such a foundation for modern scientific computation, in which most algorithms—with origins in Newton, Euler, Gauss, et al.—are real number algorithms. In 1989, Mike Shub, Steve Smale, and I introduced a theory of computation and complexity over an arbitrary ring or field R [BSS89]. If R is Z2 = ({0, 1},+,·), the classical computer science theory is recovered. If R is the field of real numbers R, Newton’s algorithm, the paradigm algorithm of numerical analysis, fits naturally into our model of computation. Complexity classes P, NP and the fundamental question “Does P=NP? ” can be formulated naturally over an arbitrary ring R. The answer to the fundamental question depends in general on the complexity of deciding feasibility of polynomial systems over R. When R is Z2, this becomes the classical satisfiability problem of Cook–Levin [Cook71, Levin73]. When R is the field of complex numbers C, the answer depends on the complexity of Hilbert’s Nullstellensatz. The notion of reduction between problems (e.g., between traveling salesman and satisfiability) has

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Is it possible for two intelligent beings to communicate meaningfully, without any common language or background? This question has interest on its own, but is especially relevant in the context of modern computational infrastructures where an increase in the diversity of computers is making the task of inter-computer interaction increasingly burdensome. Computers spend a substantial amount of time updating their software to increase their knowledge of other computing devices. In turn, for any pair of communicating devices, one has to design software that enables the two to talk to each other. Is it possible instead to let the two computing entities use their intelligence (universality as computers) to learn each others ’ behavior and attain a common understanding? What is “common understanding? ” We explore this question in this paper. To formalize this problem, we suggest that one should study the “goal of communication: ” why are the two entities interacting with each other, and what do they hope to gain by it? We propose that by considering this question explicitly, one can make progress on the question of universal communication. We start by considering a computational setting for the problem where the goal of one of the interacting players is to gain some computational wisdom from the other player. We show that if the second player is “sufficiently ” helpful and powerful, then the first player can gain significant computational power (deciding PSPACE complete languages). Our work highlights some of the definitional issues underlying the task of formalizing universal communication, but also suggests some interesting phenomena and highlights potential tools that may be used for such communication.

We study the average-case hardness of the class NP against algorithms in P. We prove that there exists some constant µ> 0 such that if there is some language in NP for which no deterministic polynomial time algorithm can decide L correctly on a 1 − (log n) −µ fraction of inputs of length n, then there is a language L ′ in NP for which no deterministic polynomial time algorithm can decide L ′ correctly on a 3/4 + (log n) −µ fraction of inputs of length n. In coding theoretic terms, we give a construction of a monotone code that can be uniquely decoded up to by a deterministic local decoder. error rate 1 4