Rewriting Systems over Unranked Trees

Finite graphs constitute an important tool in various fields of computer science. In order to transfer the theory of finite graphs at least partially to infinite systems, a finite representation of infinite systems is needed. Rewriting systems form a practical model for the finite representation of infinite graphs. Among attractive subclasses of rewriting systems is the class of ground tree rewriting systems over ranked trees, which is known to have good algorithmic properties. We investigate these algorithmic properties for two kinds of rewriting systems over unranked trees. For the first introduced rewriting formalism, we define a reduction to ranked (binary) trees via an encoding and also to standard ground tree rewriting, and we show that the generated classes of transition graphs coincide. For the second introduced rewriting formalism over unranked trees using subtree rewriting combined with flat prefix rewriting, we obtain strictly more transition graphs, and we show that the reachability problem over such graphs is still decidable. Here, a flat prefix rewrite rule substitutes a prefix of the word derived from the front of a subtree of height 1. However, as opposed to standard ground tree rewriting systems, this decidability result fails for both formalisms when the transition graphs are restricted by a deterministic top down tree automaton.