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Complexity: A Language-Theoretic Point of View

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Abstract

The theory of computation and complexity theory are fundamental parts of current theoretical computer science. They study the borders between possible and impossible in information processing, quantitative rules governing discrete computations (how much work (computational resources) has to be done (have to be used) and suffices (suffice) to algorithmically solve various computing problems), algorithmical aspects of complexity, optimization, approximation, reducibility, simulation, communication, knowledge representation, information, etc. Historically, theoretical computer science started in the 1930s with the theory of computation (computability theory) giving the exact formal border between algorithmically solvable computing problems and problems which cannot be solved by any program (algorithm). The birth of complexity theory can be set in the 1960s when computers started to be widely used and the inner difficulty of computing problems started to be investigated. At that time people defined quantitative complexity measures enabling one to compare the efficiency of computer programs and to study the computational hardness of computing problems as an inherent property of problems. The abstract part of complexity theory has tried to classify computing problems according to their hardness (computational complexity) while the algorithmic part of complexity theory has dealt with the development of methods for the design of effective algorithms for concrete problems.

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Authors
  1. Cristian Calude
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  2. Juraj Hromkovič
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Editors and Affiliations

  1. Department of Computer Science, Leiden University, P.O. Box 9512, NL-2300 RA, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Department of Computer Science, University of Colorado at Boulder, Campus 430, 80309, Boulder, CO, USA

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science Data City, FIN-20520, Turku, Finland

    Arto Salomaa

  4. Academy of Finland and Turku Centre for Computer Science (TUCS), Lemninkäisenkatu 14 A, FIN-20520, Turku, Finland

    Arto Salomaa

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© 1997 Springer-Verlag Berlin Heidelberg

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Calude, C., Hromkovič, J. (1997). Complexity: A Language-Theoretic Point of View. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07675-0_1

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  • DOI: https://doi.org/10.1007/978-3-662-07675-0_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08230-6

  • Online ISBN: 978-3-662-07675-0

  • eBook Packages: Springer Book Archive

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