Abstract
We present \(\mathsf {MSO}\) and \(\mathsf {FO}\) logics with predicates ‘between’ and ‘neighbour’ that characterise various fragments of the class of regular languages that are closed under the reverse operation. The standard connections that exist between \(\mathsf {MSO}\) and \(\mathsf {FO}\) logics and varieties of finite semigroups extend to this setting with semigroups extended with an involution. The case is different for \(\mathsf {FO}\) with neighbour relation where we show that one needs additional equations to characterise the class.
Partly supported by UMI ReLaX. The work was carried out at Chennai Mathematical Institute.
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Gastin, P., Manuel, A., Govind, R. (2019). Logics for Reversible Regular Languages and Semigroups with Involution. In: Hofman, P., Skrzypczak, M. (eds) Developments in Language Theory. DLT 2019. Lecture Notes in Computer Science(), vol 11647. Springer, Cham. https://doi.org/10.1007/978-3-030-24886-4_13
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