On systems of word equations with simple loop sets

  • Authors:

  • tpán Holub;Juha Kortelainen

  • Affiliations:

  • Department of Algebra, Charles University in Prague, Sokolovska 83, Praha 8, 186 75, Czech Republic;Department of Information Processing Science, University of Oulu, Oulu, Finland

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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Abstract

Consider the infinite system S of word equations {x"0u"1^ix"1u"2^ix"2...u"m^ix"m=y"0v"1^iy"1v"2^iy"2...v"n^iy"n|i@?N}. For each k@?N, let T"k be the subsystem of S given by i@?{k,k+1,k+2}. We prove two properties of the above system. (1)Let k=1. If @f is a solution of T"k such that primitive roots of @f(u"1),@f(u"2),...,@f(u"m) are of equal length, as well as primitive roots of @f(v"1),@f(v"2),...,@f(v"n), then @f is a solution of the whole S. (2)If n=1 then, for any k=2, a solution @f of T"k is also a solution of S.