Uniform inevitability is tree automaton ineffable
Information Processing Letters
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A modal fixpoint logic with chop
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Experimental evaluation of classical automata constructions
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Antichains: a new algorithm for checking universality of finite automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
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We present a model checking algorithm for HFL1, the firstorder fragment of Higher-Order Fixpoint Logic. This logic is capable of expressing many interesting properties which are not regular and, hence, not expressible in the modal µ-calculus. The algorithm avoids best-case exponential behaviour by localising the computation of functions and can be implemented symbolically using BDDs. We show how insight into the behaviour of this procedure, when run on a fixed formula, can be used to obtain specialised algorithms for particular problems. This yields, for example, the competitive antichain algorithm for NFA universality but also a new algorithm for a string matching problem.