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Monoid alternatives
Monoid is a mathematical solution set that is closed under an associative binary operation and has an identity element, known as commutative monoid as well. In math, the associative property is a property of some binary operations, which means that rearranging the parenthesis in an expression will not change the result. They are semigroups with identity; such algebraic structures occur in several branches of math—for example, the function from a set into itself from a monoid with respect to function composition.
In computer science and programming, the set of strings built from a given set of characters is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines, and Trace and History Monoids provide a foundation for process calculi and concurrent computing. In theoretical computer science, the study of monoids is fundamental for automata theory.









