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One-Directional Non-Counting Languages
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Idempotencies received a great deal of interest §through a problem stated by Burnside in 1902: Is §every group, which satisfies the identity x^r=1 and §has a finite set of generators, finite? In the §context of Formal Languages, the derived problem of §non-counting classes, also called Brzozowski''s §Problem, remained open for over 30 years. We treat a §variant of this, where the relations in question can §be applied only in one direction. That is, they §always increase or decrease a word''s length. The §main motivation for this came from the field of DNA §computation. The operation of duplication, which §plays a role there, is just one particular case of §such a relation. In contrast to non-counting §classes, here many of the arising languages are not §regular but rather complex. Thus many interesting §problems remain to be solved.
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