The Turing Machine Paradigm in Contemporary Computing

Jan van Leeuwen and Jiří Wiedermann

A chapter in Mathematics Unlimited — 2001 and Beyond, 2001, pp 1139-1155 from Springer

Abstract: Abstract The importance of algorithms is now recognized in all mathematical sciences, thanks to the development of computability and computational complexity theory in the 20th century. The basic understanding of computability theory developed in the nineteen thirties with the pioneering work of mathematicians like Gödel, Church, Turing and Post. Their work provided the mathematical basis for the study of algorithms as a formalized concept. The work of Hartmanis, Stearns, Karp, Cook and others in the nineteen sixties and seventies showed that the refinement of the theory to resource-bounded computations gave the means to explain the many intuitions concerning the complexity or ‘hardness’ of algorithmic problems in a precise and rigorous framework.

Date: 2001
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DOI: 10.1007/978-3-642-56478-9_59

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