Higher-Order Pushdown Trees Are Easy
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
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
Types and higher-order recursion schemes for verification of higher-order programs
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Complexity of Model Checking Recursion Schemes for Fragments of the Modal Mu-Calculus
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Model-checking higher-order functions
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
A Type System Equivalent to the Modal Mu-Calculus Model Checking of Higher-Order Recursion Schemes
LICS '09 Proceedings of the 2009 24th 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
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Higher-order recursion schemes (recursion schemes, for short) are expressive grammars for describing infinite trees. The modal μ -calculus model checking problem for recursion schemes ("Given a recursion scheme G and a modal μ -calculus formula φ , does the tree generated by G satisfy φ ?") has been a hot research topic in the theoretical community for recent years [1,2,3,4,5,6,7]. In 2006, it has been shown to be decidable, and n -EXPTIME complete (where n is the order of a recursion scheme) by Ong [5]. The model checking of recursion schemes has recently turned out to be a good basis for verification of higher-order functional programs, just as finite state model checking for programs with while-loops, and pushdown model checking for programs with first-order recursion. First, various program analysis/verification problems such as reachability, flow analysis, and resource usage verification (or equivalently, type-state checking) can be easily transformed into model-checking problems for recursion schemes [8]. Combined with a model checking algorithm for recursion schemes, this yields a sound, complete, and automated verification method for the simply-typed *** -calculus with recursion and finite base types such as booleans. Secondly, despite the extremely high worst-case time complexity (i.e. n -EXPTIME completeness) of the model checking problem for recursion schemes, our type-based model-checking algorithm [9] turned out to run reasonably fast for realistic programs. We have implemented a prototype model checker for recursion schemes TRecS , and are currently working to construct a software model checker for a subset of ML on top of it. The talk will summarize our recent results [8,9,10,11] on the model checking of recursion schemes as well as its applications to higher-order program verification, and discuss future perspectives.