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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 compute and al ..."
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Cited by 9 (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...
A Kahn principle for networks of nonmonotonic realtime processes
, 1992
"... We show that the inputoutput function computed by a network of asynchronous realtime processes is denoted by the unique fixed point of a Scott continuous functional even though the network or its components may compute a discontinuous function. This extends a wellknown principle of Kahn [Kahn, 1 ..."
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We show that the inputoutput function computed by a network of asynchronous realtime processes is denoted by the unique fixed point of a Scott continuous functional even though the network or its components may compute a discontinuous function. This extends a wellknown principle of Kahn [Kahn, 1974] to an important class of parallel systems that has resisted the traditional fixed point approach. We present a fully abstract ordertheoretic denotational semantics for networks of asynchronous realtime processes. The timesensitive nature of the component processes allows them to compute functions which are not Scott continuous, nor even monotonic, on the domain of timed message streams ordered by the usual prefix relation. Because of the discontinuous behavior of the components, the characterization of networks with nonmonotonic processes as fixed points of continuous functionals (the standard approach of denotational semantics, applied to untimed networks of monotonic processes by K...
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 function is ex ..."
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Cited by 3 (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
Enforcing Behavior with Contracts
, 2000
"... Contracts have been introduced earlier as a way of modeling a collection of agents that work within the limits set by the contract. We have analyzed the question of when an agent or a coalition of agents can reach a stated goal, despite potentially hostile behavior by the other agents. In this paper ..."
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Cited by 1 (1 self)
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Contracts have been introduced earlier as a way of modeling a collection of agents that work within the limits set by the contract. We have analyzed the question of when an agent or a coalition of agents can reach a stated goal, despite potentially hostile behavior by the other agents. In this paper, we extend the model so that we can also study whether a coalition of agents can enforce a certain temporal behavior when executing a contract. We show how to reduce this question to the question of whether a given goal can be achieved. We introduce a generalization of the action system notation that allows both angelic and demonic scheduling of actions. This allows us to model concurrent systems and interactive systems in the same framework, and show that one can be seen as the dual of the other. We analyze enforcement of temporal behavior in the case of action systems, and show that these provide for simpler proof obligations that what we get in the general case. Finally, we give three illustrative examples of how to model and analyze interactive and concurrent systems with this approach.
A GameTheoretic, Concurrent and Fair Model of the Typed LambdaCalculus, With Full Recursion
"... 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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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
Modeling Component Environments and Interactive Programs Using Iterative Choice
, 1998
"... The unifying ground for componentbased systems and interactive programs is the interaction between the user and the system or between a component and its environment. Modeling both kinds of systems in a formal framework appears to be critical for reasoning about the systems' reliability and correct ..."
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The unifying ground for componentbased systems and interactive programs is the interaction between the user and the system or between a component and its environment. Modeling both kinds of systems in a formal framework appears to be critical for reasoning about the systems' reliability and correctness. A mathematical foundation, based on the idea of contracts, permits this kind of reasoning. In this paper we study the iterative choice statement which models an event loop allowing the user to repeatedly choose from a number of actions an alternative which is enabled and have it executed. We study the properties of this statement and demonstrate its modeling capabilities by specifying an interactive dialog box, and a component environment which describes all actions the environment can take on a component. Keywords: Modeling, componentbased systems, interactive programs, contracts, angelic iteration, iterative choice, correctness, refinement TUCS Research Group Programming Methodolog...
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 compute and also ..."
Abstract
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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]), 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...
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 explain better the ..."
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