Computer Aided Verification

Volume 4144 of the series Lecture Notes in Computer Science pp 329-342

Languages of Nested Trees

  • Rajeev AlurAffiliated withUniversity of Pennsylvania
  • , Swarat ChaudhuriAffiliated withUniversity of Pennsylvania
  • , P. MadhusudanAffiliated withUniversity of Illinois at Urbana-Champaign

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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.