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arXiv · 1609.04092

Alternation Is Strict For Higher-Order Modal Fixpoint Logic

Florian Bruse
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Abstract

We study the expressive power of Alternating Parity Krivine Automata (APKA), which provide operational semantics to Higher-Order Modal Fixpoint Logic (HFL). APKA consist of ordinary parity automata extended by a variation of the Krivine Abstract Machine. We show that the number and parity of priorities available to an APKA form a proper hierarchy of expressive power as in the modal mu-calculus. This also induces a strict alternation hierarchy on HFL. The proof follows Arnold's (1999) encoding of runs into trees and subsequent use of the Banach Fixpoint Theorem.

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Florian Bruse. 2016-09-14. Alternation Is Strict For Higher-Order Modal Fixpoint Logic. https://doi.org/10.4204/eptcs.226.8

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