by Ondřej Klíma, Jiří Srba, August 1999, 14 pages.
FIMU-RS-99-02. Available as Postscript, PDF.
A pattern equation is a word equation of the form X=A where X is a sequence of variables and A is a sequence of constants. The problem whether X=A has a solution in a free idempotent semigroup (free band) is shown to be NP--complete.
by Ivana Černá, Ondřej Klíma, Jiří Srba, This is a full version of the paper accepted to SOFSEM`99. July 1999, 11 pages.
FIMU-RS-99-01. Available as Postscript, PDF.
Word equation in a special form X=A, where X is a sequence of variables and A is a sequence of constants, is considered. The problem whether X=A has a solution over a free monoid (PATTERN EQUATION problem) is shown to be NP--complete. It is also shown that disjunction of a special type equation systems and conjunction of the general ones can be eliminated. Finally, the case of stuttering equations where the word identity is read modulo xx=x is mentioned.