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On Founding the Theory of Algorithms
, 1998
"... machines and implementations The first definition of an abstract machine was given by Turing, in the classic [20]. Without repeating here the wellknown definition (e.g., see [6]), 13 we recall that each Turing machine M is equipped with a "semiinfinite tape" which it uses both to comp ..."
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Cited by 10 (4 self)
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machines and implementations The first definition of an abstract machine was given by Turing, in the classic [20]. Without repeating here the wellknown definition (e.g., see [6]), 13 we recall that each Turing machine M is equipped with a "semiinfinite tape" which it uses both to compute and also to communicate with its environment: To determine the value f(n) (if any) of the partial function 14 f : N * N computed by M , we put n on the tape in some standard way, e.g., by placing n + 1 consecutive 1s at its beginning; we start the machine in some specified, initial, internal state q 0 and looking at the leftmost end of the tape; and we wait until the machine stops (if it does), at which time the value f(n) can be read off the tape, by counting the successive 1s at the left end. Turing argued that the numbertheoretic functions which can (in principle) be computed by any deterministic, physical device are exactly those which can be computed by a Turing machine, and the correspon...
The Logic Of Functional Recursion
, 1997
"... this paper are related to "program verification" very much like predicate logic and its completeness are related to axiomatic set theory; they are certainly relevant, but not of much help in establishing specific, concrete results. In its most general form, a recursive definition of a func ..."
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Cited by 4 (2 self)
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this paper are related to "program verification" very much like predicate logic and its completeness are related to axiomatic set theory; they are certainly relevant, but not of much help in establishing specific, concrete results. In its most general form, a recursive definition of a function is expressed by a fixpoint equation of the form
A gametheoretic, concurrent and fair model of the typed lambdacalculus, with full recursion
 In CSL '97, LNCS 1414
, 1998
"... This paper, and the talk on which it is based, were strongly influenced by two, contradictory words of advice. First, there is GianCarlo Rota’s eloquent injunction in [17] to “publish the same result often”; and so I will take some time to describe again and (I hope) motivate and explain better the ..."
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Cited by 1 (0 self)
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This paper, and the talk on which it is based, were strongly influenced by two, contradictory words of advice. First, there is GianCarlo Rota’s eloquent injunction in [17] to “publish the same result often”; and so I will take some time to describe again and (I hope) motivate and explain better the gametheoretic model of concurrency, with fair merge and full recursion introduced in [7] and further studied in [9,8, 10,12]. Second, there is this young computer scientist friend of mine, who complaints about conferences in which “everyone presents a finished, polished paper on what they did the year before, so that the talks are stylized and do not lead to meaningful interaction among the participants”; and so I put off writing the paper until after the meeting, and I spent all my time up to it perfecting as best I could the new theorem I wanted to present. Still not quite what I would like to prove, this result adds products and function spaces to the constructions of [7,9], which then yield a concurrent model of the typed λcalculus which still accommodates fairness and full recursion. As it happened, gametheoretic semantics of highertype languages were featured prominently
A GameTheoretic, Concurrent and Fair Model
"... This paper, and the talk on which it is based, were strongly influenced by two, contradictory words of advice. First, there is GianCarlo Rota's eloquent injunction in [17] to "publish the same result often"; and so I will take some time to describe again and (I hope) motivate and exp ..."
Abstract
 Add to MetaCart
This paper, and the talk on which it is based, were strongly influenced by two, contradictory words of advice. First, there is GianCarlo Rota's eloquent injunction in [17] to "publish the same result often"; and so I will take some time to describe again and (I hope) motivate and explain better the gametheoretic model of concurrency, with fair merge and full recursion introduced in [7] and further studied in [9, 8, 10, 12]. Second, there is this young computer scientist friend of mine, who complaints about conferences in which "everyone presents a finished, polished paper on what they did the year before, so that the talks are stylized and do not lead to meaningful interaction among the participants"; and so I put off writing the paper until after the meeting, and I spent all my time up to it perfecting as best I could the new theorem I wanted to present. Still not quite what I would like to prove, this result adds products and function spaces to the constructions of [7, 9], which then yield a concurrent model of the typed calculus which still accommodates fairness and full recursion. As it happened, gametheoretic semantics of highertype languages were featured prominently in this conference, quite different from mine, to be sure, but, still, not entirely unrelated, and so my unconventional choice for structuring the talk and this paper made good sense in the end
On Founding the Theory of Algorithms
, 1998
"... machines and implementations The first definition of an abstract machine was given by Turing, in the classic [20]. Without repeating here the wellknown definition (e.g., see [6]), we recall that each Turing machine M is equipped with a "semiinfinite tape" which it uses both to comput ..."
Abstract
 Add to MetaCart
machines and implementations The first definition of an abstract machine was given by Turing, in the classic [20]. Without repeating here the wellknown definition (e.g., see [6]), we recall that each Turing machine M is equipped with a "semiinfinite tape" which it uses both to compute and also to communicate with its environment: To determine the value f(n) (if any) of the partial function f : N * N computed by M , we put n on the tape in some standard way, e.g., by placing n + 1 consecutive 1s at its beginning; we start the machine in some specified, initial, internal state q 0 and looking at the leftmost end of the tape; and we wait until the machine stops (if it does), at which time the value f(n) can be read off the tape, by counting the successive 1s at the left end. Turing argued that the numbertheoretic functions which can (in principle) be computed by any deterministic, physical device are exactly those which can be computed by a Turing machine, and the corresponding version of this claim for partial functions has come to be known as the ChurchTuring Thesis, because an equivalent claim was made by Church at about the same time. Turing's brilliant analysis of "mechanical computation" in [20] and a huge body of work in the last sixty years has established the truth of the ChurchTuring Thesis beyond reasonable doubt; it is of immense importance in the derivation of foundationally significant undecidability results from technical theorems about Turing machines, and it has been called "the first natural law of pure mathematics." Turing machines capture the notion of mechanical computability of numbertheoretic functions, by the ChurchTuring Thesis, but they do not model faith It has also been suggested that we do not need algorithms, only the equival...