A. Slisenko

1969

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Abstract

Let Rυ denote a set of all words of the form x1 *...* xυ, where x1,..., xυ are duplexes‡ (υ ≥ 1). The letters X, Y, Z,U will be used as variables for elements of the set Rυ. Writing x1 *...* xυ = y1 *...* yυ, will mean that \(x_i \mathop = \limits_B y_i (1 \leqslant i \leqslant \upsilon )\) (the symbol “=” will also be used to denote the equality of sets). We call a function on Rυ every algorithm f such that $$ \forall X\left( {f\left( X \right)_ \in ^ + real\;duplex} \right)\& \forall XY\left( {X = Y \supset f\left( X \right) = f\left( Y \right)} \right). $$

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