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14
The Dimensions of Individual Strings and Sequences
 INFORMATION AND COMPUTATION
, 2003
"... A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive dimension is used to assign every individual (infinite, binary ..."
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Cited by 93 (10 self)
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A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive dimension is used to assign every individual (infinite, binary) sequence S a dimension, which is a real number dim(S) in the interval [0, 1]. Sequences that
Optimal Ordered Problem Solver
, 2002
"... We present a novel, general, optimally fast, incremental way of searching for a universal algorithm that solves each task in a sequence of tasks. The Optimal Ordered Problem Solver (OOPS) continually organizes and exploits previously found solutions to earlier tasks, eciently searching not only the ..."
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Cited by 62 (20 self)
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We present a novel, general, optimally fast, incremental way of searching for a universal algorithm that solves each task in a sequence of tasks. The Optimal Ordered Problem Solver (OOPS) continually organizes and exploits previously found solutions to earlier tasks, eciently searching not only the space of domainspecific algorithms, but also the space of search algorithms. Essentially we extend the principles of optimal nonincremental universal search to build an incremental universal learner that is able to improve itself through experience.
The Speed Prior: A New Simplicity Measure Yielding NearOptimal Computable Predictions
 Proceedings of the 15th Annual Conference on Computational Learning Theory (COLT 2002), Lecture Notes in Artificial Intelligence
, 2002
"... Solomonoff's optimal but noncomputable method for inductive inference assumes that observation sequences x are drawn from an recursive prior distribution p(x). Instead of using the unknown p() he predicts using the celebrated universal enumerable prior M() which for all exceeds any recursive p() ..."
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Cited by 51 (20 self)
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Solomonoff's optimal but noncomputable method for inductive inference assumes that observation sequences x are drawn from an recursive prior distribution p(x). Instead of using the unknown p() he predicts using the celebrated universal enumerable prior M() which for all exceeds any recursive p(), save for a constant factor independent of x. The simplicity measure M() naturally implements "Occam's razor " and is closely related to the Kolmogorov complexity of . However, M assigns high probability to certain data that are extremely hard to compute. This does not match our intuitive notion of simplicity. Here we suggest a more plausible measure derived from the fastest way of computing data. In absence of contrarian evidence, we assume that the physical world is generated by a computational process, and that any possibly infinite sequence of observations is therefore computable in the limit (this assumption is more radical and stronger than Solomonoff's).
Hierarchies Of Generalized Kolmogorov Complexities And Nonenumerable Universal Measures Computable In The Limit
 INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
, 2000
"... The traditional theory of Kolmogorov complexity and algorithmic probability focuses on monotone Turing machines with oneway writeonly output tape. This naturally leads to the universal enumerable SolomonoLevin measure. Here we introduce more general, nonenumerable but cumulatively enumerable m ..."
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Cited by 38 (20 self)
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The traditional theory of Kolmogorov complexity and algorithmic probability focuses on monotone Turing machines with oneway writeonly output tape. This naturally leads to the universal enumerable SolomonoLevin measure. Here we introduce more general, nonenumerable but cumulatively enumerable measures (CEMs) derived from Turing machines with lexicographically nondecreasing output and random input, and even more general approximable measures and distributions computable in the limit. We obtain a natural hierarchy of generalizations of algorithmic probability and Kolmogorov complexity, suggesting that the "true" information content of some (possibly in nite) bitstring x is the size of the shortest nonhalting program that converges to x and nothing but x on a Turing machine that can edit its previous outputs. Among other things we show that there are objects computable in the limit yet more random than Chaitin's "number of wisdom" Omega, that any approximable measure of x is small for any x lacking a short description, that there is no universal approximable distribution, that there is a universal CEM, and that any nonenumerable CEM of x is small for any x lacking a short enumerating program. We briey mention consequences for universes sampled from such priors.
Exploring the Predictable
, 2002
"... Details of complex event sequences are often not predictable, but their reduced abstract representations are. I study an embedded active learner that can limit its predictions to almost arbitrary computable aspects of spatiotemporal events. It constructs probabilistic algorithms that (1) control in ..."
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Cited by 23 (10 self)
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Details of complex event sequences are often not predictable, but their reduced abstract representations are. I study an embedded active learner that can limit its predictions to almost arbitrary computable aspects of spatiotemporal events. It constructs probabilistic algorithms that (1) control interaction with the world, (2) map event sequences to abstract internal representations (IRs), (3) predict IRs from IRs computed earlier. Its goal is to create novel algorithms generating IRs useful for correct IR predictions, without wasting time on those learned before. This requires an adaptive novelty measure which is implemented by a coevolutionary scheme involving two competing modules collectively designing (initially random) algorithms representing experiments. Using special instructions, the modules can bet on the outcome of IR predictions computed by algorithms they have agreed upon. If their opinions dier then the system checks who's right, punishes the loser (the surprised one), and rewards the winner. An evolutionary or reinforcement learning algorithm forces each module to maximize reward. This motivates both modules to lure each other into agreeing upon experiments involving predictions that surprise it. Since each module essentially can veto experiments it does not consider profitable, the system is motivated to focus on those computable aspects of the environment where both modules still have confident but different opinions. Once both share the same opinion on a particular issue (via the loser's learning process, e.g., the winner is simply copied onto the loser), the winner loses a source of reward  an incentive to shift the focus of interest onto novel experiments. My simulations include an example where surprisegeneration of this kind helps to speed up ...
Gödel Machines: SelfReferential Universal Problem Solvers Making Provably Optimal SelfImprovements
, 2003
"... An old dream of computer scientists is to build an optimally ecient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Gödel's celebrated selfreferential formulas (1931). Our Godel machine's initial software includes an axiomat ..."
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Cited by 16 (7 self)
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An old dream of computer scientists is to build an optimally ecient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Gödel's celebrated selfreferential formulas (1931). Our Godel machine's initial software includes an axiomatic description of: the Godel machine's hardware, the problemspeci c utility function (such as the expected future reward of a robot), known aspects of the environment, costs of actions and computations, and the initial software itself (this is possible without introducing circularity). It also includes a typically suboptimal initial problemsolving policy and an asymptotically optimal proof searcher searching the space of computable proof techniquesthat is, programs whose outputs are proofs. Unlike previous approaches, the selfreferential Gödel machine will rewrite any part of its software, including axioms and proof searcher, as soon as it has found a proof that this will improve its future performance, given its typically limited computational resources. We show that selfrewrites are globally optimalno local minima!since provably none of all the alternative rewrites and proofs (those that could be found by continuing the proof search) are worth waiting for.
The New AI: General & Sound & Relevant for Physics
, 2003
"... Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inducti ..."
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Cited by 15 (9 self)
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Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inductive inference based on Occam's razor, problem solving, decision making, and reinforcement learning in environments of a very general type. Since inductive inference is at the heart of all inductive sciences, some of the results are relevant not only for AI and computer science but also for physics, provoking nontraditional predictions based on Zuse's thesis of the computergenerated universe.
OpenEnded Artificial Evolution
, 2001
"... Of all the issues discussed at Alife VII: Looking Forward, Looking Backward, the issue of whether it was possible to create an arti cial life system that exhibits openended evolution of novelty is by far the biggest. ..."
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Cited by 8 (3 self)
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Of all the issues discussed at Alife VII: Looking Forward, Looking Backward, the issue of whether it was possible to create an arti cial life system that exhibits openended evolution of novelty is by far the biggest.
Musical Qualia, Context, Time, and Emotion
 Journal of Consciousness Studies
, 2004
"... Nearly all listeners consider the subjective aspects of music, such as its emotional tone, to have primary importance. But contemporary philosophers often downplay, ignore, or even deny such aspects of experience. Moreover, traditional philosophies of music try to decontextualize it. Using music ..."
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Cited by 6 (3 self)
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Nearly all listeners consider the subjective aspects of music, such as its emotional tone, to have primary importance. But contemporary philosophers often downplay, ignore, or even deny such aspects of experience. Moreover, traditional philosophies of music try to decontextualize it. Using music as an example, this paper explores the structure of qualitative experience, demonstrating that it is multilayer emergent, noncompositional, enacted, and situation dependent, among other nonCartesian properties.
A Kolmogorov Complexitybased Genetic Programming Tool for String Compression
 in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2000), Darrell Whitley, David Goldberg, Erick CantuPaz, Lee Spector, Ian Parmee, and HansGeorg Beyer, Eds., Las Vegas
, 2000
"... By following the guidelines set in one of our previous papers, in this paper we face the problem of Kolmogorov complexity estimate for binary strings by making use of a Genetic Programming approach. This consists in evolving a population of Lisp programs looking for the "optimal" program that genera ..."
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Cited by 3 (0 self)
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By following the guidelines set in one of our previous papers, in this paper we face the problem of Kolmogorov complexity estimate for binary strings by making use of a Genetic Programming approach. This consists in evolving a population of Lisp programs looking for the "optimal" program that generates a given string. By taking into account several target binary strings belonging to different formal languages, we show the effectiveness of our approach in obtaining an approximation from the above of the Kolmogorov complexity function. Moreover, the adequate choice of "similar" target strings allows our system to show very interesting computational strategies. Experimental results indicate that our tool achieves promising compression rates for binary strings belonging to formal languages. Furthermore, even for more complicated strings our method can work, provided that some degree of loss is accepted. These results constitute a first step in using Kolmogorov complexit...