Model-Checking Infinite Systems Generated by Ground Tree Rewriting

  • Authors:
  • Christof Löding

  • Affiliations:
  • -

  • Venue:
  • FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
  • Year:
  • 2002

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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.