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International Conference on Language and Automata Theory and Applications

LATA 2011: Language and Automata Theory and Applications pp 1–21Cite as

Green’s Relations and Their Use in Automata Theory

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6638))

Abstract

The objective of this survey is to present the ideal theory of monoids, the so-called Green’s relations, and to illustrate the usefulness of this tool for solving automata related questions.

We use Green’s relations for proving four classical results related to automata theory: The result of Schützenberger characterizing star-free languages, the theorem of factorization forests of Simon, the characterization of infinite words of decidable monadic theory due to Semenov, and the r esult of determinization of automata over infinite words of McNaughton.

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Author information

Authors and Affiliations

  1. LIAFA/CNRS/Université Paris Diderot, Paris 7, France

    Thomas Colcombet

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  1. Thomas Colcombet
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Department of Informatics, Kyushu University, 744 Motooka, 819–0395, Fukuoka, Japan

    Shunsuke Inenaga

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Colcombet, T. (2011). Green’s Relations and Their Use in Automata Theory. In: Dediu, AH., Inenaga, S., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2011. Lecture Notes in Computer Science, vol 6638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21254-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-21254-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21253-6

  • Online ISBN: 978-3-642-21254-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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