On full abstraction for PCF: I, II, and III
Information and Computation
Higher-Order Pushdown Trees Are Easy
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
On Model-Checking Trees Generated by Higher-Order Recursion Schemes
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Deciding monadic theories of hyperalgebraic trees
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Unsafe grammars and panic automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The monadic second order theory of trees given by arbitrary level-two recursion schemes is decidable
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Semantics of higher-order recursion schemes
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Hierarchies of infinite structures generated by pushdown automata and recursion schemes
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type hierarchy upon this interpretation of the base type gives a finite semantics for simply-typed lambda-trees. A calculus based on this semantics is proven sound and complete. In particular, for regular infinite lambda-trees it is decidable whether a given automaton has a run or not. As regular lambda-trees are precisely recursion schemes, this decidability result holds for arbitrary recursion schemes of arbitrary level, without any syntactical restriction. This partially solves an open problem of Knapik, Niwinski and Urzyczyn.