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Selected Papers

  • Book
  • © 1982

Overview

Authors:
  1. Calvin C. Elgot

    1. Mathematical Sciences Department, IBM Watson Research Center, Yorktown Heights, USA

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Editors:
  1. Stephen L. Bloom

    1. Department of Pure and Applied Mathematics, Stevens Institute of Technology, Hoboken, USA

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Part I

    1. Realization of Events by Logical Nets

      • Irving M. Copi, Calvin C. Elgot, Jesse B. Wright
      Pages 1-16

    2. Random-Access Stored-Program Machines, an Approach to Programming Languages

      • Calvin C. Elgot, Abraham Robinson
      Pages 17-51

    3. Abstract Algorithms and Diagram Closure

      • Calvin C. Elgot
      Pages 53-138

  3. Part II

    1. Algebraic Theories and Program Schemes

      • Calvin C. Elgot
      Pages 139-156

    2. The Common Algebraic Structure of Exit-Automata and Machines

      • Calvin C. Elgot
      Pages 157-178

    3. Monadic Computation and Iterative Algebraic Theories

      • Calvin C. Elgot
      Pages 179-234

    4. On the Algebraic Structure of Rooted Trees

      • Calvin C. Elgot, Stephen L. Bloom, Ralph Tindell
      Pages 236-273

    5. Solutions of the Iteration Equation and Extensions of the Scalar Iteration Operation

      • Stephen L. Bloom, Calvin C. Elgot, Jesse B. Wright
      Pages 275-295

    6. Vector Iteration in Pointed Iterative Theories

      • Stephen L. Bloom, Calvin C. Elgot, Jesse B. Wright
      Pages 297-312

  4. Part III

    1. Structured Programming With and Without GO TO Statements

      • Calvin C. Elgot
      Pages 313-325

    2. A Semantically Meaningful Characterization of Reducible Flowchart Schemes

      • Calvin C. Elgot, John C. Shepherdson
      Pages 327-359

    3. An Equational Axiomatization of the Algebra of Reducible Flowchart Schemes

      • Calvin C. Elgot, John C. Shepherdson
      Pages 361-409

  5. Part IV

    1. On Coordinated Sequential Processes

      • Calvin C. Elgot, Raymond E. Miller
      Pages 411-460

  6. Erratum to: Erratum and Corrigendum for “Structured Programming With and Without GO TO Statements”

    1. Erratum to: Erratum and Corrigendum for “Structured Programming With and Without GO TO Statements”

      • Calvin C. Elgot
      Pages 461-461

  7. Back Matter

    Pages 456-460
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Keywords

About this book

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.

Authors, Editors and Affiliations

  • Department of Pure and Applied Mathematics, Stevens Institute of Technology, Hoboken, USA

    Stephen L. Bloom

  • Mathematical Sciences Department, IBM Watson Research Center, Yorktown Heights, USA

    Calvin C. Elgot

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