This paper reviews algorithmic information theory, which is an attempt to apply information-theoretic and probabilistic ideas to recursive function theory. Typical concerns in this approach are, for example, the number of bits of information required to specify an algorithm, or the probability that a program whose bits are chosen by coin flipping produces a given output. During the past few years the definitions of algorithmic information theory have been reformulated. The basic features of the new formalism are presented here and certain results of R. M. Solovay are reported.

Most simulations of biological evolution depend on a rather restricted set of properties. In this paper a richer model, based on differential gene expression is introduced to control developmental processes in an artificial evolutionary system. Differential gene expression is used to get different cell types and to modulate cell division and cell death. One of the advantages using developmental processes in evolutionary systems is the reduction of the information needed in the genome to encode e.g. shapes or cell types which results in better scaling behavior of the system. My result showed that the shaping of multicellular organisms in 3d is possible with the proposed system.

Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For period-doubling and band-merging cascades, we derive expressions for the entropy, the interdependence of-machine complexity and entropy, and the latent complexity of the transition to chaos. At the transition deterministic finite automaton models diverge in size. Although there is no regular or context-free Chomsky grammar in this case, we give finite descriptions at the higher computational level of context-free Lindenmayer systems. We construct a restricted indexed context-free grammar and its associated one-way nondeterministic nested stack automaton for the cascade limit language. This analysis of a family of dynamical systems suggests a complexity theoretic description of phase transitions based on the informational diversity and computational complexity of observed data that is independent of particular system control parameters. The approach gives a much more refined picture of the architecture of critical states than is available via

We obtain some dramatic results using statistical mechanics--thermodynamics kinds of arguments concerning randomness, chaos, unpredictability, and uncertainty in mathematics. We construct an equation involving only whole numbers and addition, multiplication, and exponentiation, with the property that if one varies a parameter and asks whether the number of solutions is finite or infinite, the answer to this question is indistinguishable from the result of independent tosses of a fair coin. This yields a number of powerful Godel incompleteness-type results concerning the limitations of the axiomatic method, in which entropy--information measures are used. c fl 1987 Academic Press, Inc. 2 G. J. Chaitin 1. Introduction It is now half a century since Turing published his remarkable paper On Computable Numbers, with an Application to the Entscheidungsproblem (Turing [15]). In that paper Turing constructs a universal Turing machine that can simulate any other Turing machine. He also use...

This paper describes new genetic and developmental principles for an artificial evolutionary system (AES) and reports the first simulation results. Emphasis is placed on those developmental processes which reduce the length of the genome to code for a given problem. We exemplify the usefulness of developmental processes with cell growth, cell differentiation and the creation of neural control structures which we used to control a real world autonomous agent. The importance of including developmental processes relies much on the fact that a neural network can be specified implicitly by using cell-to-cell communication. 1 Introduction In the field of autonomous agents different approaches have been studied: One of them, the evolutionary approach, aims to produce increasingly sophisticated autonomous agents with no need to care about the details of the robots control structure. As others,(Nolfi et al.,1994; Cangelosi et al.,1994; Daellert & Beer,1994; Harvey et al.,1995), we are convinc...

INTRODUCTION We will cover two topics First, Algorithmic Probability --- the motivation for defining it, how it overcomes di#culties in other formulations of probability, some of its characteristic properties and successful applications. Second, we will apply it to problems in A.I. --- where it promises to give near optimum search procedures for two very broad classes of problems. A strong motivation for revising classical concepts of probability has come from the analysis of human problem solving. When working on a di#cult problem, a person is in a maze in which he must make choices of possible courses of action. If the problem is a familiar one, the choices will all be easy. If it is not familiar, there can be much uncertainty in each choice, but choices must somehow be made. One basis for choice might be the probability of each choice leading to a quick solution --- this probability being based on experience in this problem and in problems like it. A good reason for using proba

A practical measure for the complexity of sequences of symbols (“strings”) is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles of sequences, for which it reverts to the difference between the maximal entropy of the ensemble and the actual entropy given the specific environment within which the sequence is to be interpreted. Thus, the physical complexity measures the amount of information about the environment that is coded in the sequence, and is conditional on such an environment. In practice, an estimate of the complexity of a string can be obtained by counting the number of loci per string that are fixed in the ensemble, while the volatile positions represent, again with respect to the environment, randomness. We apply this measure to tRNA sequence data.

We have employed Algorithmic Probability Theory to construct a system for machine learning of great power and generality. The principal thrust of present research is the design of sequences of problems to train this system. Current programs for machine learning are limited in the kinds of concepts accessible to them, the kinds of problems they can learn to solve, and in the efficiency with which they learn — both in computation time needed and/or in amount of data needed for learning. Algorithmic Probability Theory provides a general model of the learning process that enables us to understand and surpass many of these limitations. Starting with a machine containing a small set of concepts, we use a carefully designed sequence of problems of increasing difficulty to bring the machine to a high level of problem solving skill. The use of training sequences of problems for machine knowledge acquisition promises to yield Expert Systems that will be easier to train and free of the brittleness that characterizes the narrow specialization of present day systems of this sort. It is also expected that the present research will give needed insight in the design of training sequences for human learning.

Abstract—In this paper and attached video, we present a third-generation expert system named Knowledge Amplification by Structured Expert Randomization (KASER) for which a patent has been filed by the U.S. Navy’s SPAWAR Systems Center, San Diego, CA (SSC SD). KASER is a creative expert system. It is capable of deductive, inductive, and mixed derivations. Its qualitative creativity is realized by using a tree-search mechanism. The system achieves creative reasoning by using a declarative representation of knowledge consisting of object trees and inheritance. KASER computes with words and phrases. It possesses a capability for metaphor-based explanations. This capability is useful in explaining its creative suggestions and serves to augment the capabilities provided by the explanation subsystems of conventional expert systems. KASER also exhibits an accelerated capability to learn. However,

The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin’s famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of the strength of the theory. I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental.