Associative Binary Operations of Order-Decreasing Full Terms
Abstract
Order-decreasing full terms are special types of terms derived from order-decreasing full transformations on a finite chain (1,…,n) and variables from an alphabet Xn . The set of all order-decreasing full terms is closed under the superposition operation such that the superassociative law holds. In this work, three binary operations on the set of all order-decreasing full terms of type tn induced by the superposition are defined and the satisfaction with associative property is proved. We also consider tree languages of order-decreasing full terms and define their operation. Embedding theorems of semigroups of order-decreasing full terms into semigroups of tree languages constructed from order-decreasing full terms are provided.References
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