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Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms
 Proceedings of the Sixth International Conference on Genetic Algorithms
, 1995
"... A measure of search difficulty, fitness distance correlation (FDC), is introduced and examined in relation to genetic algorithm (GA) performance. In many cases, this correlation can be used to predict the performance of a GA on problems with known global maxima. It correctly classifies easy deceptiv ..."
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Cited by 204 (5 self)
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A measure of search difficulty, fitness distance correlation (FDC), is introduced and examined in relation to genetic algorithm (GA) performance. In many cases, this correlation can be used to predict the performance of a GA on problems with known global maxima. It correctly classifies easy deceptive problems as easy and difficult nondeceptive problems as difficult, indicates when Gray coding will prove better than binary coding, and is consistent with the surprises encountered when GAs were used on the Tanese and royal road functions. The FDC measure is a consequence of an investigation into the connection between GAs and heuristic search. 1 INTRODUCTION A correspondence between evolutionary algorithms and heuristic state space search is developed in (Jones, 1995b). This is based on a model of fitness landscapes as directed, labeled graphs that are closely related to the state spaces employed in heuristic search. We examine one aspect of this correspondence, the relationship between...
Beyond The Universal Turing Machine
, 1998
"... We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of welldefined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a phi ..."
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Cited by 28 (1 self)
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We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of welldefined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.
Information and Computation: Classical and Quantum Aspects
 REVIEWS OF MODERN PHYSICS
, 2001
"... Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely ..."
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Cited by 23 (2 self)
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Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental
Reverse Hillclimbing, Genetic Algorithms and the Busy Beaver Problem
 In Forrest, S. (Ed.), Genetic Algorithms: Proceedings of the Fifth International Conference (ICGA93
, 1993
"... This paper introduces a new analysis tool called reverse hillclimbing, and demonstrates how it can be used to evaluate the performance of a genetic algorithm. Using reverse hillclimbing, one can calculate the exact probability that hillclimbing will attain some point in a landscape. From this, the e ..."
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Cited by 17 (1 self)
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This paper introduces a new analysis tool called reverse hillclimbing, and demonstrates how it can be used to evaluate the performance of a genetic algorithm. Using reverse hillclimbing, one can calculate the exact probability that hillclimbing will attain some point in a landscape. From this, the expected number of evaluations before the point is found by hillclimbing can be calculated. This figure can be compared to the average number of evaluations done by a genetic algorithm. This procedure is illustrated using the Busy Beaver problem, an interesting problem of theoretical importance in its own right. At first sight, a genetic algorithm appears to perform very well on this landscape, after examining only a vanishingly small proportion of the space. Closer examination reveals that the number of evaluations it performs to discover an optimal solution compares poorly with even the simplest form of hillclimbing. Finally, several other uses for reverse hillclimbing are discussed. 3 San...
The many forms of hypercomputation
 Applied Mathematics and Computation
, 2006
"... This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess. ..."
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Cited by 16 (0 self)
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This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess.
Cognition Is Not Computation: The Argument From Irreversibility
, 1996
"... The dominant scientific and philosophical view of the mind  according to which, put starkly, cognition is computation  is refuted herein, via specification and defense of the following new argument: Computation is reversible; cognition isn't; ergo, cognition isn't computation. After presenting ..."
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Cited by 7 (6 self)
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The dominant scientific and philosophical view of the mind  according to which, put starkly, cognition is computation  is refuted herein, via specification and defense of the following new argument: Computation is reversible; cognition isn't; ergo, cognition isn't computation. After presenting a sustained dialectic arising from this defense, we conclude with a brief preview of the view we would put in place of the cognitioniscomputation doctrine. We are indebted to Bill Rapaport, Pat Hayes, Ken Ford, Marvin Minsky, Jim Fahey, two anonymous referees (who provided particularly insightful comments), and many Rensselaer students. These people provided trenchant objections which saw to the evolution of the present version from a rather inauspicious primogenitor. 1 Introduction The dominant scientific and philosophical view of the mind  put starkly, that cognition is computation  is refuted herein, via specification and defense of the following new argument: Computation is...
Resistance is Futile; Formal Linguistic Observations on Design Patterns
, 1997
"... Inspection of the current literature on Design Patterns shows that the Prime Directive for this community is Pragmatics. It hardly matters what patterns are, or how Patterns are represented formally or syntactically. What does matter is their role in enhancing the reuse of good solutions to recurrin ..."
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Cited by 5 (0 self)
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Inspection of the current literature on Design Patterns shows that the Prime Directive for this community is Pragmatics. It hardly matters what patterns are, or how Patterns are represented formally or syntactically. What does matter is their role in enhancing the reuse of good solutions to recurring problems. In this article I want to show that minimal assumptions about the pragmatic use of Patterns suffice to show that Design Patterns form just another formal language, which can be shown to be at least Recursively enumerable. Whether the language is Recursive depends on further conditions on the actual relation which is assumed to hold between a pattern and its possible invocations. There are no a priori reasons enforcing that this should be an easily decidable relation; quite to the contrary: a little amount of linguistic expressivity suffices for showing that this relation is likely to be complex. Without restrictions on the linguistic tools allowed for expressing design patterns t...
Effective Computability of Solutions of Differential Inclusions The Ten Thousand Monkeys Approach
"... Abstract: In this paper we consider the computability of the solution of the initialvalue problem for differential inclusions with semicontinuous righthand side. We present algorithms for the computation of the solution using the “ten thousand monkeys” approach, in which we generate all possible so ..."
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Cited by 5 (2 self)
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Abstract: In this paper we consider the computability of the solution of the initialvalue problem for differential inclusions with semicontinuous righthand side. We present algorithms for the computation of the solution using the “ten thousand monkeys” approach, in which we generate all possible solution tubes, and then check which are valid. In this way, we show that the solution of an uppersemicontinuous differential inclusion is uppersemicomputable, and the solution of a differential inclusion defined by a onesided locally Lipschitz function is lowersemicomputable computable. We show that the solution of a locally Lipschitz differential equation is computable even if the function is not effectively locally Lipschitz. We also recover a result of Ruohonen, in which it is shown that if the solution is unique, then it is computable, even if the righthand side is not locally Lipschitz. We also prove that the maximal interval of existence for the solution must be effectively enumerable open, and give an example of a computable locally Lipschitz function which is not effectively locally Lipschitz.
Genetic Algorithms and Heuristic Search
 Santa Fe Institute
, 1995
"... Genetic algorithms (GAs) and heuristic search are shown to be structurally similar. The strength of the correspondence and its practical consequences are demonstrated by considering the relationship between fitness functions in GAs and the heuristic functions of AI. By examining the extent to which ..."
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Cited by 4 (2 self)
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Genetic algorithms (GAs) and heuristic search are shown to be structurally similar. The strength of the correspondence and its practical consequences are demonstrated by considering the relationship between fitness functions in GAs and the heuristic functions of AI. By examining the extent to which fitness functions approximate an AI ideal, a measure of GA search difficulty is defined and applied to previously studied problems. The success of the measure in predicting GA performance (1) illustrates the potential advantages of viewing evolutionary search from a heuristic search perspective and (2) appears to be an important step towards answering a question that has been the subject of much research in the GAs community: what makes search hard (or easy) for a GA? Submitted to the International Joint Conference on Artificial Intelligence. 1 Introduction The primary aim of this paper is to establish a connection between genetic algorithms (GAs) and heuristic search. The foundation of t...
An argument for the uncomputability of infinitary mathematical expertise
 ‘Expertise in Context’, AAAI Press, Menlo Park, CA
, 1997
"... To a majority of the people involved in the study of expertise from a computational perspective, `expertise' tends to refer to domains such as medical diagnosis, aircraft piloting, auditing, etc. The reasoning in domains like these appears to be readymade for computational packaging. But what if we ..."
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Cited by 4 (3 self)
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To a majority of the people involved in the study of expertise from a computational perspective, `expertise' tends to refer to domains such as medical diagnosis, aircraft piloting, auditing, etc. The reasoning in domains like these appears to be readymade for computational packaging. But what if we try to cast a broader, braver net in an attempt to catch varieties of expertise out there in the real world which don't, at least at first glance, look like they can be rendered in computational terms? In particular, what about mathematical expertise? In this chapter I focus on elementary "infinitary " expertise in the domain of mathematical logic. I argue that at least some of this expertise is indeed uncomputable. I end by briefly discussing the implications of this argument for the practice of AI and expert systems.