Acta Mathematica Sinica, English Series

, Volume 29, Issue 3, pp 571-590

First online:

On the finite basis problem for certain 2-limited words

  • Jian Rong LiAffiliated withDepartment of Mathematics, Lanzhou University
  • , Wen Ting ZhangAffiliated withDepartment of Mathematics, Lanzhou University Email author 
  • , Yan Feng LuoAffiliated withDepartment of Mathematics, Lanzhou University

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Let X* be a free monoid over an alphabet X and W be a finite language over X. Let S(W) be the Rees quotient X*/I(W), where I(W) is the ideal of X* consisting of all elements of X* that are not subwords of W. Then S(W) is a finite monoid with zero and is called the discrete syntactic monoid of W. W is called finitely based if the monoid S(W) is finitely based. In this paper, we give some sufficient conditions for a monoid to be non-finitely based. Using these conditions and other results, we describe all finitely based 2-limited words over a three-element alphabet. Furthermore, an explicit algorithm is given to decide that whether or not a 2-limited word in which there are exactly two non-linear letters is finitely based.


Finite basis problem 2-limited words discrete syntactic monoid

MR(2000) Subject Classification

20M07 08B05