Weakly Regular Relations and Applications

. A new class of tree-tuple languages is introduced : the weakly regular relations. It is an extension of the regular case (regular relations) and a restriction of tree-tuple synchronized languages, that has all usual nice properties, except closure under complement. Two applications are presented : to unication modulo a rewrite system, and to one-step rewriting.

Weakly Regular Relations and Applications

Abstract A new class of tree-tuple languages is introduced: the weakly regular relations. It is an extension of the regular case (regular relations) and a restriction of treetuple synchronized languages, that has all usual nice properties, except closure by complement. Two applications are presented: to unification modulo a rewrite system, and to one-step rewriting. 1 Introduction Several classes of tree-tuple languages (also viewed as tree relations), have been defined by means of automata or grammars. In particular, a simple one, the Regular Relations (RR), consists in defining regularity as being the one of the tree language (over the productalphabet) obtained by overlapping the tuple components