Abstract
In this paper we prove that for each k, the expressive power of k-ary fixed-point logic, i.e. the fragment of fixed-point logic whose fixed-point operators are restricted to arity ≤ k, strictly exceeds the power of (k − 1)-ary fixed-point logic. This solves a problem that was posed by Chandra and Harel in 1982.
Our proof has a rather general form that applies to several variants of fixed-point logic and also to transitive-closure logic.
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© 1994 Springer-Verlag Berlin Heidelberg
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Grohe, M. (1994). Bounded-arity hierarchies in fixed-point logics. In: Börger, E., Gurevich, Y., Meinke, K. (eds) Computer Science Logic. CSL 1993. Lecture Notes in Computer Science, vol 832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049330
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DOI: https://doi.org/10.1007/BFb0049330
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