1. Dual Adjunction Between $\Omega$-Automata and Wilke Algebra Quotients
- Author
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Chernev, Anton, Hansen, Helle Hvid, and Kupke, Clemens
- Subjects
Computer Science - Formal Languages and Automata Theory - Abstract
$\Omega$-automata and Wilke algebras are formalisms for characterising $\omega$-regular languages via their ultimately periodic words. $\Omega$-automata read finite representations of ultimately periodic words, called lassos, and they are a subclass of lasso automata. We introduce lasso semigroups as a generalisation of Wilke algebras that mirrors how lasso automata generalise $\Omega$-automata, and we show that finite lasso semigroups characterise regular lasso languages. We then show a dual adjunction between lasso automata and quotients of the free lasso semigroup with a recognising set, and as our main result we show that this dual adjunction restricts to one between $\Omega$-automata and quotients of the free Wilke algebra with a recognising set.
- Published
- 2024