On one-pass term rewriting - Fülöp Zoltán (Acta cybernetica, 1999)
Two restricted ways to apply a term rewriting system (TRS) to a tree are considered. When the one-pass root-started, strategy is followed, rewriting starts from the root and continues stepwise towards the leaves without ever rewriting a paxt of the current tree produced in a previous rewrite step. Onepass leaf-started, rewriting is defined similarly, but rewriting begins from the leaves. In the sentential form inclusion problem one asks whether all trees which can be obtained with a given TRS from the trees of some regular tree language T belong to another given regular tree language U, and in the normal form inclusion problem the same question is asked about the normal forms of T. We show that for a left-linear TRS these problems can be decided for both of our one-pass strategies. In all four cases the decision algorithm involves the construction of a suitable tree recognizer.