Proof Systems for the Modal $$\mu $$-Calculus Obtained by Determinizing Automata

Abstract Automata operating on infinite objects feature prominently in the theory of modal $$\mu $$ -calculus. One such application concerns tableau games introduced by Niwiński & Walukiewicz, which winning condition for plays can be naturally checked a nondeterministic parity stream automaton. Inspired work Jungteerapanich and Stirling we show how determinization constructions this automaton may used to directly obtain proof systems More concretely, introduce binary tree construction determinizing automata. Using define annotated cyclic system $$\textsf{BT}$$ , where formulas are tuples strings. Soundness Completeness follow almost immediately from correctness method.