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Mathematical Models of Interactive Computing
, 1999
"... : Finite computing agents that interact with an environment are shown to be more expressive than Turing machines according to a notion of expressiveness that measures problemsolving ability and is specified by observation equivalence. Sequential interactive models of objects, agents, and embedded s ..."
Abstract

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: Finite computing agents that interact with an environment are shown to be more expressive than Turing machines according to a notion of expressiveness that measures problemsolving ability and is specified by observation equivalence. Sequential interactive models of objects, agents, and embedded systems are shown to be more expressive than algorithms. Multiagent (distributed) models of coordination, collaboration, and true concurrency are shown to be more expressive than sequential models. The technology shift from algorithms to interaction is expressed by a mathematical paradigm shift that extends inductive definition and reasoning methods for finite agents to coinductive methods of set theory and algebra. An introduction to models of interactive computing is followed by an account of mathematical models of sequential interaction in terms of coinductive methods of nonwellfounded set theory, coalgebras, and bisimulation. Models of distributed information flow and multiagent inter...
Church’s Thesis and the Conceptual Analysis of Computability
 Notre Dame Journal of Formal Logic
, 2007
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1 Introduction to Complexity Theory
"... “Complexity theory ” is the body of knowledge concerning fundamental principles of computation. Its beginnings can be traced way back in history to the use of asymptotic complexity and reducibility by the Babylonians. Modern complexity theory is the result of research activities in many different fi ..."
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“Complexity theory ” is the body of knowledge concerning fundamental principles of computation. Its beginnings can be traced way back in history to the use of asymptotic complexity and reducibility by the Babylonians. Modern complexity theory is the result of research activities in many different fields: biologists studying models for neuron nets or evolution, electrical engineers
Incomputability after Alan Turing
"... The year 2012 marks the 100th anniversary of the birth of Alan Turing. The following two articles were inspired by the work ..."
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The year 2012 marks the 100th anniversary of the birth of Alan Turing. The following two articles were inspired by the work