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From Tree Automata to String Automata Minimization

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Abstract

In this paper, we propose a reduction of the minimization problem for a bottom-up deterministic tree automaton (DFTA), making the latter a minimization of a string deterministic finite automaton (DFA). To achieve this purpose, we proceed first by the transformation of the tree automaton into a particular string automaton, followed by minimizing this string automaton. In addition, we show that for our transformation, the minimization of the resulting string automaton coincides with the minimization of the original tree automaton. Finally, we discuss the complexity of our proposal for different types of tree automata, namely: standard, acyclic, incremental, and incrementally constructed tree automata.

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Notes

  1. Similar approaches are being taken by several other tree automata researchers.

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Acknowledgments

This work is supported by a South Africa-Algeria Cooperation Project funded by the South African NRF under project 87462 and the Algerian MESRS-DGRSDT under project A/AS-2013-002. Any opinion, finding and conclusion or recommendation expressed in this material is that of the author(s) and the NRF/MESRS-DGRSDT do not accept any liability in this regard.

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Authors and Affiliations

  1. Laboratoire LIM, Université Amar Telidji, Laghouat, Algérie

    Younes Guellouma & Hadda Cherroun

  2. Laboratoire LITIS - EA 4108, Normandie Université, Rouen, France

    Djelloul Ziadi

  3. FASTAR Group, Department of Information Science, Stellenbosch University, Stellenbosch, South Africa

    Bruce W. Watson

Authors
  1. Younes Guellouma
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  2. Hadda Cherroun
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  3. Djelloul Ziadi
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  4. Bruce W. Watson
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Correspondence to Younes Guellouma.

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Guellouma, Y., Cherroun, H., Ziadi, D. et al. From Tree Automata to String Automata Minimization. Theory Comput Syst 62, 1203–1222 (2018). https://doi.org/10.1007/s00224-017-9815-4

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  • DOI: https://doi.org/10.1007/s00224-017-9815-4

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