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.
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17 RandomAccess StoredProgram Machines an Approach
25 Abstract Algorithms and Diagram Closure
32 Algebraic Theories and Program Schemes
9 other sections not shown
algorithm argument atomic augmented matrix automata automaton base morphism begin behavior bijection C. C. Elgot CACI scheme called composition computes Corollary defined definition denoted diagram digraph disjoint edge elements equation for g equivalent exit extended finite sequence finitely determined flow-chart scheme function f functor given Gödel number graph ideal morphism ideal theory identity infinite input integers isomorphic iteration equation iterative theory k-tuples label Lemma Let f Let g machine mapping matrix morphism f natural numbers normal description notion obtained out-degree output partial function path position of g power ideal proof Proposition RASP recursive regular expression relation resp result cell rooted trees satisfies scalar iteration Section sequacious subset subtheory Suppose T-flows T-trees Theorem theory morphism tion transition relation tupling Turing machine unique solution vector iteration vertex vertices Yorktown Heights