Pattern Equations and Equations with Stuttering

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 x 2 = x is mentioned

Pattern Equations and Equations with Stuttering ⋆

Abstract. 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 x 2 = x is mentioned.