Algebraic Properties of Eulerian Words

Eulerian trails have connected automata theory, as well as formal languages, for a decade now. This paper extends to explain a new discovery based on (un)tested ideas or techniques with application in programming languages. Converting graphs to words and finding their respective automata models that accept a particular set of words as their language is one of the challenging tasks; henceforth, finding the time complexity of the algorithms. In this paper, hole-free Eulerian words are the main sets of words.