Elsevier

Theoretical Computer Science

Volume 123, Issue 2, 31 January 1994, Pages 239-258
Theoretical Computer Science

Equations and monoid varieties of dot-depth one and two

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Abstract

Each level of the Straubing's hierarchy of aperiodic monoids can be parametrized in a natural way. This paper studies this parametrization for dot-depth one and two monoids. For level one, it is shown that the mth level is defined by a finite sequence of equations if and only if m = 1, 2 or 3. For level two, and for m ⩾ 1, a sequence of equations is given which is satisfied in the mth level and shown to ultimately define the 1st level.

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This material is based upon work supported by the National Science Foundation under Grant No. CCR-9101800. The Government has certain rights in this material. Many thanks to the referees for their valuable comments and suggestions.