The Finite Basis Problem Of 2-limited Words Over A Four-element Alphabet

Let W be a finite set of words over alphabet ?.We say S(W)is the discrete syntactic monoid of W if S(W)be the Rees quotient ?*/I(W),where I(W)is the ideal of ?*consisting of all elements of ?*that are not subwords of W.The set of words W is called finitely based if the monoid S(W)is finitely based.At present,the finite base problems of 2-limited words over 2-element alphabet and 3-element alphabet have been solved and give a completeclassification.In this paper,we give a complete classification of 2-limited words over 4-element alphabet through finite base problems.