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. © 2011 Springer-Verlag.
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CITATION STYLE
Colcombet, T. (2011). Green’s relations and their use in automata theory. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6638 LNCS, pp. 1–21). Springer Verlag. https://doi.org/10.1007/978-3-642-21254-3_1
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