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On the Length of Programs for Computing Finite Binary Sequences
 Journal of the ACM
, 1966
"... The use of Turing machines for calculating finite binary sequences is studied from the point of view of information theory and the theory of recursive functions. Various results are obtained concerning the number of instructions in programs. A modified form of Turing machine is studied from the same ..."
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Cited by 226 (7 self)
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The use of Turing machines for calculating finite binary sequences is studied from the point of view of information theory and the theory of recursive functions. Various results are obtained concerning the number of instructions in programs. A modified form of Turing machine is studied from the same point of view. An application to the problem of defining a patternless sequence is proposed in terms of the concepts here 2 G. J. Chaitin developed. Introduction In this paper the Turing machine is regarded as a general purpose computer and some practical questions are asked about programming it. Given an arbitrary finite binary sequence, what is the length of the shortest program for calculating it? What are the properties of those binary sequences of a given length which require the longest programs? Do most of the binary sequences of a given length require programs of about the same length? The questions posed above are answered in Part 1. In the course of answering them, the logical ...
A Basis for a Mathematical Theory of Computation
 Computer Programming and Formal Systems
, 1963
"... edited by P. Braffort and D. Hirshberg and published by NorthHolland. ..."
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Cited by 205 (6 self)
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edited by P. Braffort and D. Hirshberg and published by NorthHolland.
Introduction to Lambda Calculus
, 1994
"... ion is said to bind the free variable x in M . E.g. we say that x:yx has x as bound and y as free variable. Substitution [x := N ] is only performed in the free occurrences of x: yx(x:x)[x := N ] yN(x:x): In calculus there is a similar variable binding. In R b a f(x; y)dx the variable x is bou ..."
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Cited by 183 (4 self)
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ion is said to bind the free variable x in M . E.g. we say that x:yx has x as bound and y as free variable. Substitution [x := N ] is only performed in the free occurrences of x: yx(x:x)[x := N ] yN(x:x): In calculus there is a similar variable binding. In R b a f(x; y)dx the variable x is bound and y is free. It does not make sense to substitute 7 for x: R b a f(7; y)d7; but substitution for y makes sense: R b a f(x; 7)dx. For reasons of hygiene it will always be assumed that the bound variables that occur in a certain expression are dierent from the free ones. This can be fullled by renaming bound variables. E.g. x:x becomes y:y. Indeed, these expressions act the same way: (x:x)a = a = (y:y)a and in fact they denote the same intended algorithm. Therefore expressions that dier only in the names of bound variables are identied. 8 Introduction to Lambda Calculus Functions of more arguments Functions of several arguments can be obtained by iteration of applica...
Logic and the Challenge of Computer Science
, 1988
"... Nowadays computer science is surpassing mathematics as the primary field of logic applications, but logic is not tuned properly to the new role. In particular, classical logic is preoccupied mostly with infinite static structures whereas many objects of interest in computer science are dynamic objec ..."
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Cited by 153 (16 self)
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Nowadays computer science is surpassing mathematics as the primary field of logic applications, but logic is not tuned properly to the new role. In particular, classical logic is preoccupied mostly with infinite static structures whereas many objects of interest in computer science are dynamic objects with bounded resources. This chapter consists of two independent parts. The first part is devoted to finite model theory; it is mostly a survey of logics tailored for computational complexity. The second part is devoted to dynamic structures with bounded resources. In particular, we use dynamic structures with bounded resources to model Pascal.
Termination proofs for systems code
 In PLDI ’06: Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
, 2006
"... Program termination is central to the process of ensuring that systems code can always react. We describe a new program termination prover that performs a pathsensitive and contextsensitive program analysis and provides capacity for large program fragments (i.e. more than 20,000 lines of code) tog ..."
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Cited by 134 (30 self)
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Program termination is central to the process of ensuring that systems code can always react. We describe a new program termination prover that performs a pathsensitive and contextsensitive program analysis and provides capacity for large program fragments (i.e. more than 20,000 lines of code) together with support for programming language features such as arbitrarily nested loops, pointers, functionpointers, sideeffects, etc. We also present experimental results on device driver dispatch routines from the Windows operating system. The most distinguishing aspect of our tool is how it shifts the balance between the two tasks of constructing and respectively checking the termination argument. Checking becomes the hard step. In this paper we show how we solve the corresponding challenge of checking with binary reachability analysis.
The Dynamical Hypothesis in Cognitive Science
 Behavioral and Brain Sciences
, 1997
"... The dynamical hypothesis is the claim that cognitive agents are dynamical systems. It stands opposed to the dominant computational hypothesis, the claim that cognitive agents are digital computers. This target article articulates the dynamical hypothesis and defends it as an open empirical alternati ..."
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Cited by 109 (1 self)
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The dynamical hypothesis is the claim that cognitive agents are dynamical systems. It stands opposed to the dominant computational hypothesis, the claim that cognitive agents are digital computers. This target article articulates the dynamical hypothesis and defends it as an open empirical alternative to the computational hypothesis. Carrying out these objectives requires extensive clarification of the conceptual terrain, with particular focus on the relation of dynamical systems to computers. Key words cognition, systems, dynamical systems, computers, computational systems, computability, modeling, time. Long Abstract The heart of the dominant computational approach in cognitive science is the hypothesis that cognitive agents are digital computers; the heart of the alternative dynamical approach is the hypothesis that cognitive agents are dynamical systems. This target article attempts to articulate the dynamical hypothesis and to defend it as an empirical alternative to the compu...
Scalable Computing
 Computer Science Today: Recent Trends and Developments
, 1996
"... . Scalable computing will, over the next few years, become the normal form of computing. In this paper we present a unified framework, based on the BSP model, which aims to serve as a foundation for this evolutionary development. A number of important techniques, tools and methodologies for the desi ..."
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Cited by 83 (3 self)
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. Scalable computing will, over the next few years, become the normal form of computing. In this paper we present a unified framework, based on the BSP model, which aims to serve as a foundation for this evolutionary development. A number of important techniques, tools and methodologies for the design of sequential algorithms and programs have been developed over the past few decades. In the transition from sequential to scalable computing we will find that new requirements such as universality and predictable performance will necessitate significant changes of emphasis in these areas. Programs for scalable computing, in addition to being fully portable, will have to be efficiently universal, offering high performance, in a predictable way, on any general purpose parallel architecture. The BSP model provides a discipline for the design of scalable programs of this kind. We outline the approach and discuss some of the issues involved. 1 Introduction For fifty years, sequential computin...
A DNA and restriction enzyme implementation of Turing Machines.
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
"... Bacteria employ restriction enzymes to cut or restrict DNA at or near specific words in a unique way. Many restriction enzymes cut the two strands of doublestranded DNA at different positions leaving overhangs of singlestranded DNA. Two pieces of DNA may be rejoined or ligated if their terminal ov ..."
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Cited by 80 (1 self)
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Bacteria employ restriction enzymes to cut or restrict DNA at or near specific words in a unique way. Many restriction enzymes cut the two strands of doublestranded DNA at different positions leaving overhangs of singlestranded DNA. Two pieces of DNA may be rejoined or ligated if their terminal overhangs are complementary. Using these operations fragments of DNA, or oligonucleotides, may be inserted and deleted from a circular piece of plasmid DNA. We propose an encoding for the transition table of a Turing machine in DNA oligonucleotides and a corresponding series of restrictions and ligations of those oligonucleotides that, when performed on circular DNA encoding an instantaneous description of a Turing machine, simulate the operation of the Turing machine encoded in those oligonucleotides. DNA based Turing machines have been proposed by Charles Bennett but they invoke imaginary enzymes to perform the statesymbol transitions. Our approach differs in that every operation can be pe...