Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Some mathematical limitations of the general-purpose analog computer
Advances in Applied Mathematics
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Complexity and real computation
Complexity and real computation
How we know what technology can do
Communications of the ACM
ACM SIGSOFT Software Engineering Notes
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
How to compare the power of computational models
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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Relations between such concepts as reducibility, universality, hardness, completeness, and deductibility are studied. The aim is to build a flexible and comprehensive theoretical foundations for different techniques and ideas used in computer science. It is demonstrated that: concepts of universality of algorithms and classes of algorithms are based on the construction of reduction of algorithms; concepts of hardness and completeness of problems are based on the construction of reduction of problems; all considered concepts of reduction, as well as deduction in logic are kinds of reduction of abstract properties. The Church-Turing Thesis, which states universality of the class of all Turing machines, is considered in a mathematical setting as a theorem proved under definite conditions.