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Fixing the State Budget: Approximation of Regular Languages with Small DFAs

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Automated Technology for Verification and Analysis (ATVA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10482))

Abstract

Strings are pervasive in programming, and arguably even more pervasive in web programming. A natural abstraction for reasoning about strings are finite-automata. They are a well-understood formalism, and operations on them are decidable and well-known. But in practice these operations either blow up in size or in cost of operations. Hence the attractive automata representations become impractical. In this paper we propose reasoning about strings using small automata, by restricting the number of states available. We show how we can construct small automata which over-approximate the language specified by a larger automata, using discrete optimization techniques, both complete approaches and incomplete approaches based on greedy search. Small automata provide a strong basis for reasoning about strings in programming, since operations on small automata do not blow up in cost.

G. Gange—This work was supported by the Australian Research Council through grants DE160100568 and LP140100437.

Pierre Ganty has been supported by the Madrid Regional Government project S2013/ICE-2731, N-Greens Software - Next-GeneRation Energy-EfficieNt Secure Software, and the Spanish Ministry of Economy and Competitiveness project No. TIN2015-71819-P, RISCO - RIgorous analysis of Sophisticated COncurrent and distributed systems.

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Notes

  1. 1.

    or a \(k-1\)-state over-approximation, on which we turn \(\delta '\) into a total function.

  2. 2.

    Note that the empty set is not a block, hence it is not part of the resulting partition.

  3. 3.

    We do not include a model for dom, as the natural decision model is semantically equivalent to the general approximation model.

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Authors and Affiliations

  1. Department of Computing and Information Systems, University of Melbourne, Melbourne, 3010, Australia

    Graeme Gange & Peter J. Stuckey

  2. IMDEA Software Institute, Madrid, Spain

    Pierre Ganty

Authors
  1. Graeme Gange
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  2. Pierre Ganty
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  3. Peter J. Stuckey
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Editors and Affiliations

  1. Indian Institute of Science, Bangalore, India

    Deepak D'Souza

  2. Chennai Mathematical Institute, Kelambakkam, India

    K. Narayan Kumar

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Gange, G., Ganty, P., Stuckey, P.J. (2017). Fixing the State Budget: Approximation of Regular Languages with Small DFAs. In: D'Souza, D., Narayan Kumar, K. (eds) Automated Technology for Verification and Analysis. ATVA 2017. Lecture Notes in Computer Science(), vol 10482. Springer, Cham. https://doi.org/10.1007/978-3-319-68167-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-68167-2_5

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  • Publisher Name: Springer, Cham

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