Scalar and Vectorial mu-calculus with Atoms
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We study an extension of modal mu-calculus to sets with atoms and we study its basic properties. Model checking is decidable on orbit-finite structures, and a correspondence to parity games holds. On the other hand, satisfiability becomes undecidable. We also show expressive limitations of atom-enriched mu-calculi, and explain how their expressive power depends on the structure of atoms used, and on the choice between basic or vectorial syntax.
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