Abstract
Omega-regular algebras axiomatise the equational theory of omega-regular expressions as induced by omega-regular language identity. Wagner presented an omega-regular algebra which requires recursively defined side conditions in some of its axioms. We introduce a first-order Horn axiomatisation for which such conditions can be avoided because additive and multiplicative units are absent. We prove its completeness relative to Wagner’s result using categorical constructions for adjoining additive and multiplicative units.
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Laurence, M.R., Struth, G. (2012). On Completeness of Omega-Regular Algebras. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_12
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DOI: https://doi.org/10.1007/978-3-642-33314-9_12
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