Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The monadic second-order logic of graphs IX: machines and their behaviours
Selected papers of the workshop on Topology and completion in semantics
Languages, automata, and logic
Handbook of formal languages, vol. 3
Fixed point characterization of infinite behavior of finite-state systems
Theoretical Computer Science
Pushdown processes: games and model-checking
Information and Computation - Special issue on FLOC '96
The evaluation of first-order substitution is monadic second-order compatible
Theoretical Computer Science
On Infinite Terms Having a Decidable Monadic Theory
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations 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
Iterated pushdown automata and complexity classes
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Deciding monadic theories of hyperalgebraic trees
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Higher order pushdown automata, the Caucal hierarchy of graphs and parity games
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Unsafe grammars and panic automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Safety is not a restriction at level 2 for string languages
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
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
Model-checking higher-order functions
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
Games on Higher Order Multi-stack Pushdown Systems
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Types and Recursion Schemes for Higher-Order Program Verification
APLAS '09 Proceedings of the 7th Asian Symposium on Programming Languages and Systems
Symbolic backwards-reachability analysis for higher-order pushdown systems
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Verification of higher-order computation: a game-semantic approach
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
An automata-theoretic approach to infinite-state systems
Time for verification
Krivine machines and higher-order schemes
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Unsafe grammars and panic automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
A finite semantics of simply-typed lambda terms for infinite runs of automata
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
On the Significance of the Collapse Operation
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Prefix rewriting for nested-words and collapsible pushdown automata
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
A saturation method for collapsible pushdown systems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Simple models for recursive schemes
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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
Recursive schemes, krivine machines, and collapsible pushdown automata
RP'12 Proceedings of the 6th international conference on Reachability Problems
Model Checking Higher-Order Programs
Journal of the ACM (JACM)
C-SHORe: a collapsible approach to higher-order verification
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
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We show that the problem of checking if an infinite tree generated by a higher-order grammar of level 2 (hyperalgebraic) satisfies a given μ-calculus formula (or, equivalently, if it is accepted by an alternating parity automaton) is decidable, actually 2-Exptime-complete. Consequently, the monadic second-order theory of any hyperalgebraic tree is decidable, so that the safety restriction can be removed from our previous decidability result. The last result has been independently obtained by Aehlig, de Miranda and Ong. Our proof goes via a characterization of possibly unsafe second-order grammars by a new variant of higher-order pushdown automata, which we call panic automata. In addition to the standard pop1 and pop2 operations, these automata have an option of a destructive move called panic. The model-checking problem is then reduced to the problem of deciding the winner in a parity game over a suitable 2nd order pushdown system.