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Computational Complexity

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Formal Languages and Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 148))

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Abstract

Computational complexity is a central field of Theoretical Computer Science and is concerned with the study of the intrinsic complexity of computational tasks. Much of complexity theory deals with decision problems and it focuses on natural computational resources. Since it depends on context what resources are deemed natural, different resources on various computational models have been studied. The most common computational resources on Turing machines are space (how much memory does it take to solve a problem) and time (how many steps does it take to solve a problem), but there are many more. Problems that need “similar” resource bounds are grouped together in complexity classes. A complexity class is specified by several parameters: (1) The underlying model of computation and its mode, (2) the resource we wish to bound, and (3) an explicit bound on this resource. Then the complexity class is defined as the set of all problems or languages decided by the computational model operating in the appropriate mode obeying the resource bound on the fixed measure.

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, D-85748, Garching bei München, Germany

    Markus Holzer

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  1. Markus Holzer
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Editors and Affiliations

  1. Research Group on Mathematical Lingustics, Rovira i Virgili University, Pl. Imperial Tàrraco 1, 43005, Tarragona, Spain

    Carlos Martín-Vide

  2. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 70109, Bucharest, Romania

    Victor Mitrana

  3. Institute of Mathematics, Romanian Academy, PO Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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Holzer, M. (2004). Computational Complexity. In: Martín-Vide, C., Mitrana, V., Păun, G. (eds) Formal Languages and Applications. Studies in Fuzziness and Soft Computing, vol 148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39886-8_12

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  • DOI: https://doi.org/10.1007/978-3-540-39886-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53554-3

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