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Model-checking infinite systems generated by ground tree rewriting. (English) Zbl 1077.68694
Nielsen, Mogens (ed.) et al., Foundations of software science and computation structures. 5th international conference, FOSSACS 2002, held as part of the joint European conferences on theory and practice of software, ETAPS 2002, Grenoble, France, April 8–12, 2002. Proceedings. Berlin: Springer (ISBN 3-540-43366-X). Lect. Notes Comput. Sci. 2303, 280-294 (2002).
Summary: 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.
For the entire collection see [Zbl 0989.00051].

##### MSC:
 68Q60 Specification and verification (program logics, model checking, etc.) 68Q42 Grammars and rewriting systems
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