# On the finite basis problem for certain 2-limited words

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DOI: 10.1007/s10114-012-0193-1

- Cite this article as:
- Li, J.R., Zhang, W.T. & Luo, Y.F. Acta. Math. Sin.-English Ser. (2013) 29: 571. doi:10.1007/s10114-012-0193-1

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## Abstract

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.