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Formal Analysis of Online Algorithms

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Book cover Automated Technology for Verification and Analysis (ATVA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6996))

Abstract

In [2], we showed how viewing online algorithms as reactive systems enables the application of ideas from formal verification to the competitive analysis of online algorithms. Our approach is based on weighted automata, which assign to each input word a cost in \({\rm I\!R}^{\geq 0}\). By relating the “unbounded look ahead” of optimal offline algorithms with nondeterminism, and relating the “no look ahead” of online algorithms with determinism, we were able to solve problems about the competitive ratio of online algorithms and the memory they require.

In this paper we improve the application in three important and technically challenging aspects. First, we allow the competitive analysis to take into account assumptions about the environment. Second, we allow the online algorithm to have a bounded lookahead. Third, we describe a symbolic version of the model-checking algorithm and demonstrate its applicability. The first two contributions broaden the scope of our approach to settings in which the traditional analysis of online algorithms is particularly complicated. The third contribution improves the practicality of our approach and enables it to handle larger state spaces.

Supported in part by the Minerva Center at the Weizmann Institute, and by an Advanced Research Grant from the ERC under the European Community’s 7th Framework Programme.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Hebrew University, Jerusalem, 91904, Israel

    Benjamin Aminof & Orna Kupferman

  2. Department of Computer Science, Weizmann Institute of Science, Rehovot, 76100, Israel

    Robby Lampert

Authors
  1. Benjamin Aminof
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  2. Orna Kupferman
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  3. Robby Lampert
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Editor information

Editors and Affiliations

  1. University of California, Santa Barbara, CA, USA

    Tevfik Bultan

  2. Department of Computer Science and Information Engineering, National Chung Cheng University, 168 University Road, Min-Hsiung, 62102, Chiayi, Taiwan, ROC

    Pao-Ann Hsiung

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Aminof, B., Kupferman, O., Lampert, R. (2011). Formal Analysis of Online Algorithms. In: Bultan, T., Hsiung, PA. (eds) Automated Technology for Verification and Analysis. ATVA 2011. Lecture Notes in Computer Science, vol 6996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24372-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-24372-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24371-4

  • Online ISBN: 978-3-642-24372-1

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