## On the system of word equations $$x^ i_ 1 x^ i_ 2\dots x^ i_ m=y^ i_ 1 y^ i_ 2\dots y^ i_ n$$ $$(i=1,2,\dots)$$ in a free monoid.(English)Zbl 0877.68073

Summary: It is proved that the system of word equation $$x^i_1= y^i_1y^i_2\dots y^i_n$$, $$i= 1,2,\dots,\lceil n/2\rceil+1$$, has only cyclic solutions. Some sharpenings concerning the cases $$n= 5, 7$$ and $$n\geq 9$$ are derived as well as results concerning the general system of equations $$x^i_1x^i_2\dots x^i_m= y^i_1y^i_2\dots y^i_n$$, $$i=1,2,\dots\;$$. Applications to test sets of certain bounded languages are considered.

### MSC:

 68Q45 Formal languages and automata

### Keywords:

system of word equation
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