Abstract
For a tree language L and a set S of term rewrite rules over Σ, the descendant of L for S is the set S ∗ ( L ) of trees reachable from a tree in L by rewriting in S. For a recognizable tree language L, we study the set D ( L ) of descendants of L for all sets of linear monadic term rewrite rules over Σ. We show that D ( L ) is finite. For each tree automaton A over Σ, we can effectively construct a set { R 1 , … , R k } of linear monadic term rewrite systems over Σ such that D ( L ( A ) ) = { R 1 ∗ ( L ( A ) ) , … , R k ∗ ( L ( A ) ) } and for any 1 ⩽ i < j ⩽ k , R i ∗ ( L ( A ) ) ≠ R j ∗ ( L ( A ) ) .
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