In this article, we consider the hierarchy of the modal μ-calculus over reflexive and symmetric graphs and show that in this class the modal μ-calculus hierarchy is infinite. In the proof, a parity game over a tree is transformed into a equivalent parity game where Duplicator, when playing over the reflexive and symmetric closure of the tree, will never use loops or back edges.
["Giovanna D'Agostino", 'Giacomo Lenzi']
On modal μ-calculus over reflexive symmetric graphs