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Preprint, Working Paper, ... |
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| Title: |
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The Variable Hierarchy for the Games mu-Calculus |
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| Author(s): |
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Walid Belkhir ( ) 1, Luigi Santocanale () 1 |
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| Abstract: |
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Parity games are combinatorial representations of closed Boolean mu-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors into a mu-calculus. As done by Berwanger et al. for the propositional modal mu-calculus, it is possible to classify parity games into levels of a hierarchy according to the number of fixed-point variables. We ask whether this hierarchy collapses w.r.t. the standard interpretation of the games mu-calculus into the class of all complete lattices. We answer this question negatively by providing, for each n >= 1, a parity game Gn with these properties: it unravels to a mu-term built up with n fixed-point variables, it is semantically equivalent to no game with strictly less than n-2 fixed-point variables. |
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| Fulltext language: |
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English |
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| Keyword(s): |
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variable hierarchy – parity games – mu-lattices |
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| Classification: |
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ACM: D.3.1 - F.3.1 - F.3.2; MSC: 06B25 |
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| Comment: |
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To appear in the journal Annals of Pure and Applied Logic |
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