Abstract
We present a model checking algorithm for HFL1, the first-order 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.
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Axelsson, R., Lange, M. (2007). Model Checking the First-Order Fragment of Higher-Order Fixpoint Logic. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_7
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DOI: https://doi.org/10.1007/978-3-540-75560-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75558-6
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