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Partial Derivative Automaton for Regular Expressions with Shuffle

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Descriptional Complexity of Formal Systems (DCFS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9118))

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Abstract

We generalize the partial derivative automaton to regular expressions with shuffle and study its size in the worst and in the average case. The number of states of the partial derivative automata is in the worst case at most \(2^m\), where \(m\) is the number of letters in the expression, while asymptotically and on average it is no more than \((\frac{4}{3})^m\).

Authors partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT under projects UID/MAT/00144/2013 and FCOMP-01-0124-FEDER-020486.

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Notes

  1. 1.

    This upper bound corresponds to the case where all unions in \(\pi (\alpha )\) are disjoint.

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Author information

Authors and Affiliations

  1. CMUP and DM, Faculdade de Ciências da Universidade do Porto, Rua Do Campo Alegre, 4169-007, Porto, Portugal

    Sabine Broda, António Machiavelo, Nelma Moreira & Rogério Reis

Authors
  1. Sabine Broda
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  2. António Machiavelo
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  3. Nelma Moreira
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  4. Rogério Reis
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Corresponding author

Correspondence to Sabine Broda .

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    Jeffrey Shallit

  2. Department of Mathematics, University of Turku, Turku, Finland

    Alexander Okhotin

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Broda, S., Machiavelo, A., Moreira, N., Reis, R. (2015). Partial Derivative Automaton for Regular Expressions with Shuffle. In: Shallit, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2015. Lecture Notes in Computer Science(), vol 9118. Springer, Cham. https://doi.org/10.1007/978-3-319-19225-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-19225-3_2

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  • Online ISBN: 978-3-319-19225-3

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