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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 ..."
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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
"... ..."
The Missing Link  Implementation And Realization of . . .
, 1999
"... The notion of computation has attracted researchers from a wide range of areas, cognitive psychology being one of them. The analogy underlying the (metaphorical) usage of "computer" in cognitive psychology can be succinctly summarized by saying that the mind is to the brain as the program ..."
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The notion of computation has attracted researchers from a wide range of areas, cognitive psychology being one of them. The analogy underlying the (metaphorical) usage of "computer" in cognitive psychology can be succinctly summarized by saying that the mind is to the brain as the program is to the hardware. Two main assumptions are buried in this analogy: 1) that the mind can somehow be understood computationally, and 2) that the same kind of relationthe implementation relationthat obtains between programs and computer hardware obtains between minds and brains too. While the first assumption has led to fertile research, the second remained mainly at the level of an assumption. Recently our
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
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
unknown title
"... 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 ..."
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1 Introduction to Complexity Theory &quot;Complexity theory &quot; 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 developing switching theory as a tool to hardware design, mathematicians working on the foundations of logic and arithmetics, linguists investigating grammars for natural languages, physicists studying the implications of building Quantum computers, and last but not least, computer scientists searching for efficient algorithms for hard problems. The course will give an introduction to some of these areas. In this lecture we introduce the notation and models necessary to follow the rest of the course. First, we introduce some basic notation. Afterwards, we discuss the question &quot;what is computation?&quot;, followed by definitions of various types of Turing machines. Afterwards, we introduce basic complexity classes for this machine and study their relationships. (??)
unknown title
"... 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 ..."
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1 Introduction to Complexity Theory &quot;Complexity theory &quot; 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 developing switching theory as a tool to hardware design, mathematicians working on the foundations of logic and arithmetics, linguists investigating grammars for natural languages, physicists studying the implications of building Quantum computers, and last but not least, computer scientists searching for efficient algorithms for hard problems. The course will give an introduction to some of these areas. In this lecture we introduce the notation and models necessary to follow the rest of the course. First, we introduce some basic notation. Afterwards, we discuss the question &quot;what is computation?&quot;, followed by definitions of various types of Turing machines. We also introduce some basic complexity classes for these machines.
doi:10.1098/rsta.2011.0335 REVIEW Formalism and intuition in computability
"... The model of recursive functions in 1934–1936 was a deductive formal system. In 1936, Turing and in 1944, Post introduced more intuitive models of Turing machines and generational systems. When they both died prematurely in 1954, their informal approach was replaced again by the very formal Kleene T ..."
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The model of recursive functions in 1934–1936 was a deductive formal system. In 1936, Turing and in 1944, Post introduced more intuitive models of Turing machines and generational systems. When they both died prematurely in 1954, their informal approach was replaced again by the very formal Kleene Tpredicate for another decade. By 1965, researchers could no longer read the papers. A second wave of intuition arose with the book by Rogers and Lachlan’s revealing papers. A third wave of intuition has arisen from 1996 to the present with a return to the original meaning of computability in the sense of Turing and Gödel, and a return of ‘recursive ’ to its original meaning of ‘inductive ’ and the founding of Computability in Europe by Cooper and others.
Frontiers and a Retrospective
, 2013
"... I would like to dedicate this paper to Michael Rabin for his 80th birthday year, albeit more than one year too late, as a humble homage to the person I consider the founding father of Computable Economics. His effectivization of the GaleStewart Game remains the model methodological contribution to ..."
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I would like to dedicate this paper to Michael Rabin for his 80th birthday year, albeit more than one year too late, as a humble homage to the person I consider the founding father of Computable Economics. His effectivization of the GaleStewart Game remains the model methodological contribution to the field for which I coined the name Computable Economics more than 20 years ago. His classic of computable economics stands in the long and distinguished tradition that goes back to classics by Zermelo, Banach & Mazur, Steinhaus and Euwe. A part of this heritage will be discussed in the main body of the paper. I should add that I have never met Michael Rabin and do not know him personally or professionally at all. I know him only through his remarkable contributions to computability and computational complexity theories.