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Simple equations on binary factorial languages
, 2008
"... We consider equations on the monoid of factorial languages on the binary alphabet. We use the notion of a canonical decomposition of a factorial language and previous results by Avgustinovich and the author to solve several simple equations on binary factorial languages including X n = Y n, the comm ..."
Abstract

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We consider equations on the monoid of factorial languages on the binary alphabet. We use the notion of a canonical decomposition of a factorial language and previous results by Avgustinovich and the author to solve several simple equations on binary factorial languages including X n = Y n, the commutation equation XY = Y X and the conjugacy equation XZ = ZY. At the end of the paper we discuss the difficulties hindering to reduce equations on factorial languages to equations on words and to enlarge the alphabet considered.