Algorithmic Properties of Structures: Selected Papers of Erwin Engeler
By: Erwin Engeler (editor)Hardback
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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.
Part 1 Axiomatics and logics of algorithmic properties: algorithmic properties of structures; formal languages - automata and structures; proof theory and the accuracy of computations. Part 2 Galois-connections and structure of problem classes: on the solvability of algorithmic problems; lower bounds by Galois theory; towards a Galois theory of algorithmic problems. Part 3 An algebraization of algorithmics: algebras and combinators; cumulative logic programs and modelling; formal models of computation in which data are processes - theory and applications; and others.
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- ID: 9789810208721
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