Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On full abstraction for PCF: I, II, and III
Information and Computation
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Higher-Order Pushdown Trees Are Easy
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Note on winning positions on pushdown games with ω-regular conditions
Information Processing Letters
Iterated pushdown automata and complexity classes
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On Model-Checking Trees Generated by Higher-Order Recursion Schemes
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Collapsible Pushdown Automata and Recursion Schemes
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Winning Regions of Higher-Order Pushdown Games
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Positional Strategies for Higher-Order Pushdown Parity Games
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Regular sets of higher-order pushdown stacks
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Krivine machines and higher-order schemes
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
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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.