Reachability on prefix-recognizable graphs
Information Processing Letters
On Bifix Systems and Generalizations
Language and Automata Theory and Applications
Recurrent Reachability Analysis in Regular Model Checking
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
The Reachability Problem over Infinite Graphs
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Model checking FO(R) over one-counter processes and beyond
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
On probabilistic parallel programs with process creation and synchronisation
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
Some perspectives of infinite-state verification
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
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We consider the transition graphs of regular ground tree (or term) rewriting systems. The vertex set of such a graph is a (possibly infinite) set of trees. Thus, with a finite tree automaton one can represent a regular set of vertices. It is known that the backward closure of sets of vertices under the rewriting relation preserves regularity, i.e., for a regular set T of vertices the set of vertices from which one can reach T can be accepted by a tree automaton. The main contribution of this paper is to lift this result to the recurrence problem, i.e., we show that the set of vertices from which one can reach infinitely often a regular set T is regular, too. Since this result is effective, it implies that the problem whether, given a tree t and a regular set T, there is a path starting in t that infinitely often reaches T, is decidable. Furthermore, it is shown that the problems whether all paths starting in t eventually (respectively, infinitely often) reach T, are undecidable. Based on the decidability result we define a fragment of temporal logic with a decidable model-checking problem for the class of regular ground tree rewriting graphs.