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On the system of word equations x i 1 x i 2…x i m=y i 1 y i 2…y i n (i=1, 2, …) in a free monoid

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Abstract.

 It is proved that the system of word equations x i 1=y i 1 y i 2…y i n , i=1, 2,…, ⌈n/2⌉ +1, has only cyclic solutions. Some sharpenings concerning the cases n=5, 7 and n≥9 are derived as well as results concerning the general system of equations x i 1 x i 2…x i m =y i 1 y i 2…y i n , i=1, 2,… . Applications to test sets of certain bounded languages are considered.

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  1. Department of Mathematical Sciences, University of Oulu, FIN-90570 Oulu, Finland, , , , , , FI

    Ismo Hakala & Juha Kortelainen

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  1. Ismo Hakala
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  2. Juha Kortelainen
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Received: 18 May 1995/2 January 1996

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Hakala, I., Kortelainen, J. On the system of word equations x i 1 x i 2…x i m=y i 1 y i 2…y i n (i=1, 2, …) in a free monoid. Acta Informatica 34, 217–230 (1997). https://doi.org/10.1007/s002360050081

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  • DOI: https://doi.org/10.1007/s002360050081

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