On One-Pass Term Rewriting

Zoltán Fülöp 1, Eija Jurvanen 2, Magnus Steinby 3, Sándor Vágvölgyi4

Dedicated to Professor Ferenc Gécseg on the occasion of his 60th birthday.

Abstract

 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 part of the current tree produced in a previous rewrite step. One-pass 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.

Footnotes:

  1 József Attila University, Department of Computer Science, H-6701 Szeged, P. O. Box 652, Hungary, Email: fulop@inf. u-szeged.hu

  2 Turku Centre for Computer Science, DataCity, Lemminkäisenkatu 14 A, FIN-20520 Turku, Finland, Email: jurvanen@utu.fi

  3 Turku Centre for Computer Science, and Department of Mathematics, University of Turku, FIN-20014 Turku, Finland, Email: steinby@utu.fi

  4 József Attila University, Department of Applied Informatics, H-6701 Szeged, P. O. Box 652, Hungary, Email: vagvolgy@inf.u-szeged.hu