Languages of nested trees

  • Authors:

  • Rajeev Alur;Swarat Chaudhuri;P. Madhusudan

  • Affiliations:

  • University of Pennsylvania;University of Pennsylvania;University of Illinois at Urbana-Champaign

  • Venue:
  • CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
  • Year:
  • 2006

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Abstract

We study languages of nested trees—structures obtained by augmenting trees with sets of nested jump-edges. These graphs can naturally model branching behaviors of pushdown programs, so that the problem of branching-time software model checking may be phrased as a membership question for such languages. We define finite-state automata accepting such languages—these automata can pass states along jump-edges as well as tree edges. We find that the model-checking problem for these automata on pushdown systems is EXPTIME-complete, and that their alternating versions are expressively equivalent to NT-μ, a recently proposed temporal logic for nested trees that can express a variety of branching-time, “context-free” requirements. We also show that monadic second order logic (MSO) cannot exploit the structure: MSO on nested trees is too strong in the sense that it has an undecidable model checking problem, and seems too weak to capture NT-μ.