Abstract
The concepts of terms and tree languages are significant tools for the development of research works in both universal algebra and theoretical computer science. In this paper, we establish a strong connection between semigroups of terms and tree languages, which provides the tools for studying monomorphisms between terms and generalized hypersubstitutions. A novel concept of a seminearring of non-deterministic generalized hypersubstitutions is introduced and some interesting properties among subsets of its are provided. Furthermore, we prove that there are monomorphisms from the power diagonal semigroup of tree languages and the monoid of generalized hypersubstitutions to the power diagonal semigroup of non-deterministic generalized hypersubstitutions and the monoid of non-deterministic generalized hypersubstitutions, respectively. Finally, the representation of terms using the theory of n-ary functions is defined. We then present the Cayley’s theorem for Menger algebra of terms, which allows us to provide a concrete example via full transformation semigroups.
Highlights
Introduction and PreliminariesPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
Introduction and PreliminariesAcademic Editor: Ivan ChajdaReceived: 3 March 2021Accepted: 24 March 2021Published: 27 March 2021Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.Licensee MDPI, Basel, Switzerland.In the classical theory of theoretical computer science, an automaton is a finite state machine which accepts certain strings of letters from a fixed base alphabet
Formal language theory is the study of properties of languages and automata
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. It was known from [12] that a formal definition of a strong hyperidentity and a strong solid variety can be given using the concept of a generalized hypersubstitution We recall such concept as follows: Let { f i | i ∈ I } be an indexed set of operation symbols of type τ where f i is ni -ary, ni is a natural number. Let HypG (τ ) be the set of all arbitrary mappings σ : { f i | i ∈ I } → Wτ ( X ), which is called a generalized hypersubstitution of type τ.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
