Interaction, Computability, and Church's Thesis (1999)
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BibTeX
@MISC{Wegner99interaction,computability,,
author = {Peter Wegner and Dina Goldin},
title = {Interaction, Computability, and Church's Thesis},
year = {1999}
}
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Abstract
: This article formalizes the claim that interactive finite computing agents are more expressive than Turing machines. The impact of models of interaction on Church's thesis and Godel's incompleteness result is explored. The evolution from algorithmic to interactive models of computation in computer architecture, software engineering, and AI is considered in a final section. Contents 1. Interaction Machines 1.1. Sequential Interaction Machines (SIMs) 1.2. Interactive Behavior and Expressiveness 1.3. Multi-Stream Interaction Machines (MIMs) 2. Extensions of Expressiveness 2.1. Interactive Extensions of Machines, Sets, and Algebras 2.2. Interactive Extensions of the Church-Turing Thesis 3. Mathematical Models of Interaction 3.1. Non-Well-Founded Set Theory 3.2. Coalgebras 3.3. Beyond Non-Well-Founded Sets 4. From Induction to Coinduction 4.1. The Inductive Modeling Paradigm 4.2. Coinduction and Greatest Fixed Points 5. Metamathematics of Coinduction 5.1. From Formal Mode...
