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- W4287179632 abstract "We give an algebraic characterisation of first-order logic with the neighbour relation, on finite words. For this, we consider languages of finite words over alphabets with an involution on them. The natural algebras for such languages are involution semigroups. To characterise the logic, we define a special kind of semidirect product of involution semigroups, called the locally hermitian product. The characterisation theorem for FO with neighbour states that a language is definable in the logic if and only if it is recognised by a locally hermitian product of an aperiodic commutative involution semigroup, and a locally trivial involution semigroup. We then define the notion of involution varieties of languages, namely classes of languages closed under Boolean operations, quotients, involution, and inverse images of involutory morphisms. An Eilenberg-type correspondence is established between involution varieties of languages and pseudovarieties of involution semigroups." @default.
- W4287179632 created "2022-07-25" @default.
- W4287179632 creator A5067969358 @default.
- W4287179632 creator A5072473577 @default.
- W4287179632 date "2021-05-19" @default.
- W4287179632 modified "2023-09-27" @default.
- W4287179632 title "An Algebraic Characterisation of First-Order Logic with Neighbour" @default.
- W4287179632 doi "https://doi.org/10.48550/arxiv.2105.09368" @default.
- W4287179632 hasPublicationYear "2021" @default.
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