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Modeling Time in Computing pp 103–149Cite as

Time in the Analysis of Algorithms

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Abstract

In this chapter, we give a concise overview of the fundamental models and results of the classic theory of computation and algorithms. In accordance with the general theme of the book, the overview highlights the characteristics of time in the traditional descriptions of software and computational processes. The chapter starts with the classic Turing machine model and with the very abstract notion of time used to measure the computational complexity of Turing machines, on which the definition of complexity classes rests. It continues with the presentation of Random Access Machines (RAM), a computational model still abstract but much closer to the architecture of real computers than the simple Turing machine. Finally, it discusses models of computation with randomized behavior, such as Markov chains and probabilistic Turing machines.

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Notes

  1. 1.

    A rigorous definition should include some regularity constraints on T(n) and S(n) as functions from \(\mathrm{I}\!\mathbb{N}\) to \(\mathrm{I}\!\mathbb{N}\); see the bibliographic remarks for references with all the omitted details.

  2. 2.

    Merely quadratic, under “reasonable” hypotheses.

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Authors and Affiliations

  1. Department of Computer Science, Zürich, Switzerland

    Carlo A. Furia

  2. Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milan, Italy

    Dino Mandrioli, Angelo Morzenti & Matteo Rossi

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  1. Carlo A. Furia
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Furia, C.A., Mandrioli, D., Morzenti, A., Rossi, M. (2012). Time in the Analysis of Algorithms. In: Modeling Time in Computing. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32332-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-32332-4_6

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