Model-checking infinite systems generated by ground tree rewriting

Abstract

We consider infinite graphs that are generated by ground tree (or term) rewriting systems. The vertices of these graphs are trees. Thus, with a finite tree automaton one can represent a regular set of vertices. It is shown that for a regular set T of vertices the set of vertices from where one can reach (respectively, infinitely often reach) the set T is again regular. Furthermore it is shown that the problems, given a tree t and a regular set T, whether all paths starting in t eventually (respectively, infinitely often) reach T, are undecidable. We then define a logic which is in some sense a maximal fragment of temporal logic with a decidable model-checking problem for the class of ground tree rewriting graphs.