Abstract
In the algebra of sequential functions which map words over (0, 1)n to words over (0, 1), we call a set M complete with respect to an equivalence relation if the subalgebra generated by M contains at least one element of any equivalence class. The paper summarizes the results with respect to some known completeness notions, such as the classical completeness, τ-completeness and Kleene-completeness which can be reformulated as completenesses with respect to some equivalence relations, and it presents some new results on completeness with respect to further equivalence relations. Moreover, we discuss the metric completeness which is nearly related to completeness with respect to an equivalence relation and can also be formulated in terms of equivalences.
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Dedicated to Gustav Burosch on the occasion of his 65th birthday
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Dassow, J. (2005). Completeness of automaton mappings with respect to equivalence relations. In: Kudryavtsev, V.B., Rosenberg, I.G., Goldstein, M. (eds) Structural Theory of Automata, Semigroups, and Universal Algebra. NATO Science Series II: Mathematics, Physics and Chemistry, vol 207. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3817-8_3
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DOI: https://doi.org/10.1007/1-4020-3817-8_3
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