On Bifix Systems and Generalizations

Motivated by problems in infinite-state verification, we study word rewriting systems that extend mixed prefix/suffix rewriting (short: bifix rewriting). We introduce several types of infix rewriting where infix replacements are subject to the condition that they have to occur next to tag symbols within a given word. Bifix rewriting is covered by the case where tags occur only as end markers. We show results on the reachability relation (or: derivation relation) of such systems depending on the possibility of removing or adding tags. Where possible we strengthen decidability of the derivation relation to the condition that regularity of sets is preserved, resp. that the derivation relation is even rational. Finally, we compare our model to ground tree rewriting systems and exhibit some differences.