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The Arity Hierarchy in the Polyadic $μ$-Calculus (1509.03018v1)
Published 10 Sep 2015 in cs.LO
Abstract: The polyadic mu-calculus is a modal fixpoint logic whose formulas define relations of nodes rather than just sets in labelled transition systems. It can express exactly the polynomial-time computable and bisimulation-invariant queries on finite graphs. In this paper we show a hierarchy result with respect to expressive power inside the polyadic mu-calculus: for every level of fixpoint alternation, greater arity of relations gives rise to higher expressive power. The proof uses a diagonalisation argument.
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