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Computability And Recursion (1996)

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by Robert I. Soare
Venue:BULLETIN OF SYMBOLIC LOGIC
Citations:44 - 1 self
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BibTeX

@ARTICLE{Soare96computabilityand,
    author = {Robert I. Soare},
    title = {Computability And Recursion},
    journal = {BULLETIN OF SYMBOLIC LOGIC},
    year = {1996},
    volume = {2},
    number = {3},
    pages = {284--321}
}

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Abstract

We consider the informal concept of "computability" or "effective calculability" andtwo of the formalisms commonly used to define it, "(Turing) computability" and "(general) recursiveness". We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. After a careful historical and conceptual analysis of computability and recursion we make several recommendations in section 7 about preserving the intensional di#erences between the concepts of "computability" and "recursion." Specifically we recommend that: the term "recursive" should no longer carry the additional meaning of "computable" or "decidable;" functions defined using Turing machines, register machines, or their variants should be calle...

Keyphrases

informal concept    register machine    general english meaning    computability theory    future content    present role    related area    exact technical definition    term recursive    intensional di erences    several recommendation    effective calculability andtwo    additional meaning    turing machine    conceptual analysis   

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