Finite alogorithmic procedures and computation theories.

Moldestad, Johan; Stoltenberg-Hansen, Viggo

doi:10.7146/math.scand.a-11853

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Abstract Models Of Computation1

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2017

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Cited by 15 publications

(1 citation statement)

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“…The following fact is easily derived from [MSHT80] (where register machines are used); see also Fenstad [Fen80, Ch. 0].…”

Section: Abstract Models Of Computationmentioning

confidence: 99%

Generalizing Computability Theory to Abstract Algebras

Tucker

Zucker

2015

Turing’s Revolution

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We present a survey of our work over the last few decades on generalizations of computability theory to many-sorted algebras. The following topics are discussed, among others: (1) abstract v concrete models of computation for such algebras; (2) computability and continuity, and the use of many-sorted topological partial algebras, containing the reals; (3) comparisons between various equivalent and distinct models of computability; (4) generalized Church-Turing theses.

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“…The following fact is easily derived from [MSHT80] (where register machines are used); see also Fenstad [Fen80, Ch. 0].…”

Section: Abstract Models Of Computationmentioning

confidence: 99%

Generalizing Computability Theory to Abstract Algebras

Tucker

Zucker

2015

Turing’s Revolution

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Nondeterministic finite algorithmic procedures as the models of abstract computability

Soloviev

1987

Fundamentals of Computation Theory

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Theses for Computation and Recursion on Concrete and Abstract Structures

Feferman

2015

Turing’s Revolution

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The main aim of this article is to examine proposed theses for computation and recursion on concrete and abstract structures. What is generally referred to as Church's Thesis or the Church-Turing Thesis (abbreviated CT here) must be restricted to concrete structures whose objects are finite symbolic configurations of one sort or another. Informal and principled arguments for CT on concrete structures are reviewed. Next, it is argued that proposed generalizations of notions of computation to abstract structures must be considered instead under the general notion of algorithm. However, there is no clear general thesis in sight for that comparable to CT, though there are certain wide classes of algorithms for which plausible theses can be stated. The article concludes with a proposed thesis RT for recursion on abstract structures.

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Finite alogorithmic procedures and computation theories.

Cited by 15 publications

References 2 publications

Generalizing Computability Theory to Abstract Algebras

Generalizing Computability Theory to Abstract Algebras

Nondeterministic finite algorithmic procedures as the models of abstract computability

Theses for Computation and Recursion on Concrete and Abstract Structures

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