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Algebra and Language Theory

Algebra and Language Theory P. M. COHN 1. Introduction In the early days of high-speed computers there was a hope that it would be possible to program a computer to translate from one language to another, and this led to an intensive study of language structure. The result has been disappointing in that we are still far from making translations by computer, but that is no cause for despair. In the first place it shows that we have underestimated the richness and intricacy of our natural languages, even when used for quite prosaic ends. Secondly, this study of language has led to mathematical models of languages which admittedly are too simple to reflect all the complexities of a natural language like English, but —quite apart from their intrinsic interest—these models are found to give a good approximation to certain programming languages. And thirdly, there has been a vigorous interaction with some parts of noncommutative algebra, with benefit to " mathematical linguist " and algebraist alike. There is an extensive literature in the field, much of it written from the point of view of automata theory, but overlapping with orthodox linguistics, communication theory, probability, logic, and even algebra. Likewise there are several excellent expositions; http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

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References (63)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/7.1.1
Publisher site
See Article on Publisher Site

Abstract

P. M. COHN 1. Introduction In the early days of high-speed computers there was a hope that it would be possible to program a computer to translate from one language to another, and this led to an intensive study of language structure. The result has been disappointing in that we are still far from making translations by computer, but that is no cause for despair. In the first place it shows that we have underestimated the richness and intricacy of our natural languages, even when used for quite prosaic ends. Secondly, this study of language has led to mathematical models of languages which admittedly are too simple to reflect all the complexities of a natural language like English, but —quite apart from their intrinsic interest—these models are found to give a good approximation to certain programming languages. And thirdly, there has been a vigorous interaction with some parts of noncommutative algebra, with benefit to " mathematical linguist " and algebraist alike. There is an extensive literature in the field, much of it written from the point of view of automata theory, but overlapping with orthodox linguistics, communication theory, probability, logic, and even algebra. Likewise there are several excellent expositions;

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Mar 1, 1975

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