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Algorithmics – Is There Hope for a Unified Theory?

(Invited Talk)

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Computer Science – Theory and Applications (CSR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6072))

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Abstract

Computer science was born with the formal definition of the notion of an algorithm. This definition provides clear limits of automatization, separating problems into algorithmically solvable problems and algorithmically unsolvable ones. The second big bang of computer science was the development of the concept of computational complexity. People recognized that problems that do not admit efficient algorithms are not solvable in practice. The search for a reasonable, clear and robust definition of the class of practically solvable algorithmic tasks started with the notion of the class \({\mathcal{P}}\) and of \({\mathcal{NP}}\)-completeness. In spite of the fact that this robust concept is still fundamental for judging the hardness of computational problems, a variety of approaches was developed for solving instances of \({\mathcal{NP}}\)-hard problems in many applications. Our 40-years short attempt to fix the fuzzy border between the practically solvable problems and the practically unsolvable ones partially reminds of the never-ending search for the definition of “life” in biology or for the definitions of matter and energy in physics. Can the search for the formal notion of “practical solvability” also become a never-ending story or is there hope for getting a well-accepted, robust definition of it? Hopefully, it is not surprising that we are not able to answer this question in this invited talk. But to deal with this question is of crucial importance, because only due to enormous effort scientists get a better and better feeling of what the fundamental notions of science like life and energy mean. In the flow of numerous technical results, we must not forget the fact that most of the essential revolutionary contributions to science were done by defining new concepts and notions.

This work was partially supported by SNF grant 200021-109252/1.

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Authors and Affiliations

  1. Department of Computer Science, ETH Zurich, Switzerland

    Juraj Hromkovič

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  1. Juraj Hromkovič
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Editors and Affiliations

  1. Dept. of Theoretical Cybernetics, Kazan State University, 420008, Kazan, Russia

    Farid Ablayev

  2. Institut für Informatik, Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

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Hromkovič, J. (2010). Algorithmics – Is There Hope for a Unified Theory?. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_17

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  • DOI: https://doi.org/10.1007/978-3-642-13182-0_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13181-3

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