On Lambda-Graph Systems for Subshifts of Subshifts
  Kengo Matsumoto has introduced lambda-graph systems and strong shift equivalence of lambda-graph systems [Doc.Math.4 (1999), 285-340]. We associate to a subshift of a subshift a lambda-graph system. The strong shift equivalence class of the associated lambda-graph system is an invariant of subsystem equivalence. Wolfgang Krieger and Kengo Matsumoto have introduced the lambda$-entropy of a lambda-graph system and have shown its invariance under strong shift equivalence [Ergod.Th.&Dynam.Sys. 24 (2004) 1155 - 1172]. A separation entropy of a subshift of a subshift is introduced as the lambda-entropy of the associated lambda-graph system. 
Wolfgang Krieger