The Equational Theory of Ω-terms for Finite R-trivial Semigroups∗
نویسنده
چکیده
A new topological representation for free profinite R-trivial semigroups in terms of spaces of vertex-labeled complete binary trees is obtained. Such a tree may be naturally folded into a finite automaton if and only if the element it represents is an ω-term. The variety of ω-semigroups generated by all finite R-trivial semigroups, with the usual interpretation of the ω-power, is then studied. A simple infinite basis of identities is exhibited and a linear-time solution of the word problem for relatively free ω-semigroups is presented. This work is also compared with recent work of Bloom and Choffrut on transfinite words.
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