An automata-theoretical characterization of the OI-hierarchy
Information and Control
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Indexed Grammars—An Extension of Context-Free Grammars
Journal of the ACM (JACM)
Higher-Order Pushdown Trees Are Easy
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Deciding monadic theories of hyperalgebraic trees
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
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 Games for Typed λ-Calculi
Electronic Notes in Theoretical Computer Science (ENTCS)
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
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
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
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
On the Significance of the Collapse Operation
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Strictness of the collapsible pushdown hierarchy
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
The IO and OI hierarchies revisited
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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Recent work by Knapik, Niwiński and Urzyczyn (in FOSSACS 2002) has revived interest in the connexions between higher-order grammars and higher-order pushdown automata. Both devices can be viewed as definitions for term trees as well as string languages. In the latter setting we recall the extensive study by Damm (1982), and Damm and Goerdt (1986). There it was shown that a language is accepted by a level-n pushdown automaton if and only if the language is generated by a safe level-n grammar. We show that at level 2 the safety assumption may be removed. It follows that there are no inherently unsafe string languages at level 2.