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Ordinary interactive small-step algorithms, II

Ordinary interactive small-step algorithms, II This is the second in a series of three articles extending the proof of the Abstract State Machine Thesis---that arbitrary algorithms are behaviorally equivalent to abstract state machines---to algorithms that can interact with their environments during a step, rather than only between steps. As in the first article of the series, we are concerned here with ordinary, small-step, interactive algorithms. This means that the algorithms: (1) proceed in discrete, global steps, (2) perform only a bounded amount of work in each step, (3) use only such information from the environment as can be regarded as answers to queries, and (4) never complete a step until all queries from that step have been answered. After reviewing the previous article's formal description of such algorithms and the definition of behavioral equivalence, we define ordinary, interactive, small-step abstract state machines (ASMs). Except for very minor modifications, these are the machines commonly used in the ASM literature. We define their semantics in the framework of ordinary algorithms and show that they satisfy the postulates for these algorithms. This material lays the groundwork for the final article in the series, in which we shall prove the Abstract State Machine thesis for ordinary, intractive, small-step algorithms: All such algorithms are equivalent to ASMs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Ordinary interactive small-step algorithms, II

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References (27)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2007 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/1243996.1243998
Publisher site
See Article on Publisher Site

Abstract

This is the second in a series of three articles extending the proof of the Abstract State Machine Thesis---that arbitrary algorithms are behaviorally equivalent to abstract state machines---to algorithms that can interact with their environments during a step, rather than only between steps. As in the first article of the series, we are concerned here with ordinary, small-step, interactive algorithms. This means that the algorithms: (1) proceed in discrete, global steps, (2) perform only a bounded amount of work in each step, (3) use only such information from the environment as can be regarded as answers to queries, and (4) never complete a step until all queries from that step have been answered. After reviewing the previous article's formal description of such algorithms and the definition of behavioral equivalence, we define ordinary, interactive, small-step abstract state machines (ASMs). Except for very minor modifications, these are the machines commonly used in the ASM literature. We define their semantics in the framework of ordinary algorithms and show that they satisfy the postulates for these algorithms. This material lays the groundwork for the final article in the series, in which we shall prove the Abstract State Machine thesis for ordinary, intractive, small-step algorithms: All such algorithms are equivalent to ASMs.

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Jul 1, 2007

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