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Universality, Reducibility, and Completeness

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Machines, Computations, and Universality (MCU 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4664))

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Abstract

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.

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Authors and Affiliations

  1. Department of Computer Science, University of California, Los Angeles, Los Angeles, California 90095, USA

    Mark Burgin

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  1. Mark Burgin
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Jérôme Durand-Lose Maurice Margenstern

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Burgin, M. (2007). Universality, Reducibility, and Completeness. In: Durand-Lose, J., Margenstern, M. (eds) Machines, Computations, and Universality. MCU 2007. Lecture Notes in Computer Science, vol 4664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74593-8_3

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  • DOI: https://doi.org/10.1007/978-3-540-74593-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74592-1

  • Online ISBN: 978-3-540-74593-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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