On Global Model Checking Trees Generated by Higher-Order Recursion Schemes

  • Christopher Broadbent
  • Luke Ong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5504)


Higher-order recursion schemes are systems of rewrite rules on typed non-terminal symbols, which can be used to define infinite trees. The Global Modal Mu-Calculus Model Checking Problem takes as input such a recursion scheme together with a modal μ-calculus sentence and asks for a finite representation of the set of nodes in the tree generated by the scheme at which the sentence holds. Using a method that appeals to game semantics, we show that for an order-n recursion scheme, one can effectively construct a non-deterministic order-n collapsible pushdown automaton representing this set. The level of the automaton is strict in the sense that in general no non-deterministic order-(n − 1) automaton could do likewise (assuming the requisite hierarchy theorem). The question of determinisation is left open. As a corollary we can also construct an order-n collapsible pushdown automaton representing the constructible winning region of an order-n collapsible pushdown parity game.


Recursion Scheme Model Checking Game Semantics Collapsible Pushdown Automaton Parity Game 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christopher Broadbent
    • 1
  • Luke Ong
    • 1
  1. 1.Computing LaboratoryOxford UniversityUK

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