Abstract
In this survey paper, we present known results and open questions on a proper subclass of the class of regular languages. This class, denoted by \(\mathcal{W}\), is especially robust: it is closed under union, intersection, product, shuffle, left and right quotients, inverse of morphisms, length preserving morphisms and commutative closure. It can be defined as the largest positive variety of languages not containing the language (ab)*. It admits a nontrivial algebraic characterization in terms of finite ordered monoids, which implies that \(\mathcal{W}\) is decidable: given a regular language, one can effectively decide whether or not it belongs to \(\mathcal{W}\). We propose as a challenge to find a constructive description and a logical characterization of \(\mathcal{W}\).
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Gómez, A.C., Pin, JÉ. (2008). A Robust Class of Regular Languages. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_3
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DOI: https://doi.org/10.1007/978-3-540-85238-4_3
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