Algorithmic Properties Of Structures

Selected Papers Of E Engeler

By: Erwin Engeler (Editor)

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Hardcover | 1 January 1994

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268 Pages

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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.

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Non-Fiction Mathematics Algebra Engineering & Technology Civil Engineering Structural Engineering Computing & I.T.Computer Science Mathematical Theory of Computation Applied Mathematics Computer Programming & Software Development Algorithms & Data Structures

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Preface
Logics of Algorithmic Properties	p. 1
Algorithmic properties of structures	p. 3
Constructible maps	p. 21
Remarks on the theory of geometrical constructions	p. 31
Proof theory and the accuracy of computations	p. 45
Algorithmic approximations	p. 53
Structure and meaning of elementary programs	p. 73
An algorithmic model of strict finitism	p. 87
The logic of "can do"	p. 97
Galois Theory and the Structure of Problems	p. 107
On the solvability of algorithmic problems	p. 109
Towards a Galois theory of algorithmic problems	p. 131
Structural relations between programs and problems	p. 137
Lower bounds by Galois theory	p. 151
Generalized Galois theory and its application to complexity	p. 157
An Algebraization of Algorithmics	p. 183
Algebras and combinators	p. 185
Representations of varieties in combinatory algebras	p. 189
Equations in combinatory algebras	p. 199
Cumulative logic programs and modeling	p. 205
Formal models of computation in which data are processes: theory and applications	p. 217
Sketch of a new discipline of modeling	p. 231
Combinatory differential fields	p. 243
Table of Contents provided by Blackwell. All Rights Reserved.

Algorithmic Properties Of Structures

Selected Papers Of E Engeler

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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