Abstract
One of the main objectives of the algebraic theory of regular languages concerns the classification of regular languages based on Eilenberg’s variety theorem [10]. This theorem states that there exists a bijection between varieties of regular languages and varieties of finite monoids. For example, the variety of star-free regular languages (the closure of finite languages under Boolean operations and concatenation) is related to the monoid variety of aperiodic monoids (those with no nontrivial subgroups)[21].
Work supported by Québec FQRNT and NSERC of Canada.
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Beaudry, M., Lemieux, F. (2009). Faithful Loops for Aperiodic E-Ordered Monoids . In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_5
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