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Derived-Term Automata for Extended Weighted Rational Expressions

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Theoretical Aspects of Computing – ICTAC 2016 (ICTAC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9965))

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Abstract

We present an algorithm to build an automaton from a rational expression. This approach introduces support for extended weighted expressions. Inspired by derived-term based algorithms, its core relies on a different construct, rational expansions. We introduce an inductive algorithm to compute the expansion of an expression from which the automaton follows. This algorithm is independent of the size of the alphabet, and actually even supports infinite alphabets. It can easily be accommodated to generate deterministic (weighted) automata. These constructs are implemented in Vcsn, a free-software platform dedicated to weighted automata and rational expressions.

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Notes

  1. 1.

    See the interactive environment, http://vcsn-sandbox.lrde.epita.fr, or http://vcsn.lrde.epita.fr/dload/2.3/notebooks/expression.derived_term.html, its documentation, or this paper’s companion notebook, http://vcsn.lrde.epita.fr/dload/2.3/notebooks/ICTAC-2016.html.

  2. 2.

    The induction is on the length of the word u in , which is defined for all q and all words of the given length simultaneously.

  3. 3.

    Vcsn 2.2 as of 2016-05-16, compiled with Clang 3.6 with options -O3 -DNDEBUG, and run on a Mac OS X 10.11.4, Intel Core i7 2.9GHz, 8GB of RAM. Best run out of five.

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Acknowledgments

Interactions with A. Duret-Lutz, S. Lombardy, L. Saiu and J. Sakarovitch resulted in this work. Anonymous reviewers made very helpful comments. In particular, an anonymous reviewer of ICALP 2016 contributed the proof of Theorem 1, much simpler than the original one (which was still based on derivatives), and proposed the benchmark of Sect. 4.4.

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Authors and Affiliations

  1. EPITA Research and Development Laboratory (LRDE), 14-16, rue Voltaire, 94276, Le Kremlin-Bicêtre, France

    Akim Demaille

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  1. Akim Demaille
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Correspondence to Akim Demaille .

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Editors and Affiliations

  1. Universidade Federal de Pernambuco Centro de Informática, Recife, Pernambuco, Brazil

    Augusto Sampaio

  2. Deptartment of Electrical Engineering BL, National Taiwan University, Taipei, Taiwan

    Farn Wang

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Demaille, A. (2016). Derived-Term Automata for Extended Weighted Rational Expressions. In: Sampaio, A., Wang, F. (eds) Theoretical Aspects of Computing – ICTAC 2016. ICTAC 2016. Lecture Notes in Computer Science(), vol 9965. Springer, Cham. https://doi.org/10.1007/978-3-319-46750-4_20

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  • DOI: https://doi.org/10.1007/978-3-319-46750-4_20

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