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Algorithmic Properties Of Structures : Selected Papers Of E Engeler - Erwin Engeler

Algorithmic Properties Of Structures

Selected Papers Of E Engeler

By: Erwin Engeler (Editor)

Hardcover Published: 1st January 1994
ISBN: 9789810208721
Number Of Pages: 268

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The work of Erwin Engeler in the logic and algebra of computer science has been influential in the development of the discipline but has become difficult to assess due to its having appeared in different types of publications. This collection of selected papers seeks to represent an original and coherent approach to the basic interrelationships between mathematics and computer science. The volume begins with the area of enrichment of classical model theory by languages which express properties representing the outcome of hypothetical computer programmes executed in a given class of mathematical structures, and is related to questions of correctness and provability of programmes. This point of view allowed the generalization of classical Galois theory to the point of discussing the relation between structure and complexity of solution programmes for problems posed in various mathematical theories. The algebraic approach is deepened and enlarged in the later papers by showing that the algorithmic aspects of any mathematical structure can be uniformly dealt wiht by expanding these structures into combinatory algebras.

Preface
Logics of Algorithmic Propertiesp. 1
Algorithmic properties of structuresp. 3
Constructible mapsp. 21
Remarks on the theory of geometrical constructionsp. 31
Proof theory and the accuracy of computationsp. 45
Algorithmic approximationsp. 53
Structure and meaning of elementary programsp. 73
An algorithmic model of strict finitismp. 87
The logic of "can do"p. 97
Galois Theory and the Structure of Problemsp. 107
On the solvability of algorithmic problemsp. 109
Towards a Galois theory of algorithmic problemsp. 131
Structural relations between programs and problemsp. 137
Lower bounds by Galois theoryp. 151
Generalized Galois theory and its application to complexityp. 157
An Algebraization of Algorithmicsp. 183
Algebras and combinatorsp. 185
Representations of varieties in combinatory algebrasp. 189
Equations in combinatory algebrasp. 199
Cumulative logic programs and modelingp. 205
Formal models of computation in which data are processes: theory and applicationsp. 217
Sketch of a new discipline of modelingp. 231
Combinatory differential fieldsp. 243
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810208721
ISBN-10: 9810208723
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 268
Published: 1st January 1994
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 26.04 x 18.42  x 1.91
Weight (kg): 0.6

Earn 344 Qantas Points
on this Book