Abstract
(1) For any algorithm there is a calculus generating the domain of this algorithm. Moreover, (2) for any algorithm A, there is a calculus generating the set of all pairs 〈x, y〉 such that A(x) = y. On the other hand, (3) for any calculus there is an algorithm whose domain is a set generated by this calculus; and (4) any calculus generating a set of pairs 〈x, y〉 being the graph of a function can be transformed into an algorithm computing this function.
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© 1993 Springer Science+Business Media Dordrecht
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Uspensky, V., Semenov, A. (1993). Interrelations between algorithms and calculuses. In: Algorithms: Main Ideas and Applications. Mathematics and Its Applications, vol 251. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8232-2_8
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DOI: https://doi.org/10.1007/978-94-015-8232-2_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4256-9
Online ISBN: 978-94-015-8232-2
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