On mappings of terms determined by hypersubstitutions
Jorg Koppitz, Slavcho Shtrakov
TL;DR
This paper characterizes hypersubstitutions that induce bijections on all terms and explores the structure of the monoid they form, along with modifications to mappings on the set of all terms.
Contribution
It provides a complete characterization of bijective hypersubstitutions and analyzes the algebraic structure of the monoid they form.
Findings
Identified all hypersubstitutions that are bijections on terms.
Established that these hypersubstitutions form a monoid.
Explored modifications of hypersubstitutions to arbitrary mappings.
Abstract
The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions forms a monoid. On the other hand, one can modify each hypersubstitution to any mapping on the set of terms. For this we can consider mappings from the set of all hypersubstitutions into the set of all mappings on the set of all terms.
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy and Soft Set Theory · semigroups and automata theory