Selected Papers

ISBN-13: 9781461381792 / Angielski / Miękka / 2011 / 460 str.

Calvin C. Elgot; Stephen L. Bloom; Dana S. Scott

Opis

Cal Elgot was a very serious and thoughtful researcher, who with great determi- nation attempted to find basic explanations for certain mathematical phenomena- as the selection of papers in this volume well illustrate. His approach was, for the most part, rather finitist and constructivist, and he was inevitably drawn to studies of the process of computation. It seems to me that his early work on decision problems relating automata and logic, starting with his thesis under Roger Lyndon and continuing with joint work with Biichi, Wright, Copi, Rutledge, Mezei, and then later with Rabin, set the stage for his attack on the theory of computation through the abstract treatment of the notion of a machine. This is also apparent in his joint work with A. Robinson reproduced here and in his joint papers with John Shepherdson. Of course in the light of subsequent work on decision problems by Biichi, Rabin, Shelah, and many, many others, the subject has been placed on a completely different plane from what it was when Elgot left the area. But I feel that his papers, results-and style-were very definitely influential at the time and may well have altered the course of the investigation of these problems. As Sammy Eilenberg explains, the next big influence on Elgot's thinking was category theory, which gave him a way of expressing his ideas in a sharply algebraic manner. The joint book with Eilenberg is one illustration of this influence.

Spis treści

[4] Realization of Events.- [17] Random-Access Stored-Program Machines, an Approach to Programming Languages.- [25] Abstract Algorithms and Diagram Closure.- [32] Algebraic Theories and Program Schemes.- [31] The Common Algebraic Structure of Exit-Automata and Machines.- [34] Monadic Computation and Iterative Algebraic Theories.- [38] On the Algebraic Structure of Rooted Trees.- [43] Solutions of the Iteration Equation and Extensions of the Scalar Iteration Operation.- [44] Vector Iteration in Pointed Iterative Theories.- [37] Structured Programming With and Without GO TO Statements.- [42] A Semantically Meaningful Characterization of Reducible Flowchart Schemes.- [50] An Equational Axiomatization of the Algebra of Reducible Flowchart Schemes.- [48] On Coordinated Sequential Processes.