Abstract
The alternation hierarchy problem asks whether every mu-term,<br />that is a term built up using also a least fixed point constructor<br />as well as a greatest fixed point constructor, is equivalent to a<br />mu-term where the number of nested fixed point of a different type<br />is bounded by a fixed number.<br />In this paper we give a proof that the alternation hierarchy<br />for the theory of mu-lattices is strict, meaning that such number<br />does not exist if mu-terms are built up from the basic lattice <br />operations and are interpreted as expected. The proof relies on the<br />explicit characterization of free mu-lattices by means of games and<br />strategies.
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