Left-noncounting languages

AbstractLetX be a finite alphabet and letX* be the free monoid generated byX. A languageA $$ \subseteq $$ X* is called left-noncounting if there existsk ≥ 0 such that forx,y εX*,xky εA if and only ifxk+iy εA. The class of all left-noncounting languages overX forms a Boolean algebra which generally contains properly the class of all noncounting languages overX and is properly contained in the class of all power-separating languages overX. In this paper, we discuss some relations among these three classes of languages and we characterize the automata accepting the left-noncounting languages and the syn tactic monoids of the left-noncounting languages.

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