A NATURAL AXIOMATIZATION OF COMPUTABILITY AND PROOF OF CHURCH’S THESIS

by Nachum Dershowitz , Yuri Gurevich

Citations:

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Datum	Value	Source
TITLE	A NATURAL AXIOMATIZATION OF COMPUTABILITY AND PROOF OF CHURCH’S THESIS	SVM HeaderParse 0.2
AUTHOR NAME	Nachum Dershowitz	SVM HeaderParse 0.2
AUTHOR NAME	Yuri Gurevich	SVM HeaderParse 0.2
ABSTRACT	Abstract. Church’s Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turingcomputable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church’s Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing’s Thesis, characterizing the effective string functions, and—in particular—the effectively-computable functions on string representations of numbers.	SVM HeaderParse 0.2
CITATIONS	112 found	ParsCit 1.0