Equivalences for fair Kripke structures
We extend the notion of bisimulation to Kripke structures with fairness. We define equivalences that preserve fairness and are akin to bisimulation. Specifically we define an equivalence and show that it is complete in the sense that it is the coarsest equivalence that preserves the logic CTL* interpreted with respect to the fair paths. We show that the addition of fairness might cause two Kripke structures, which can be distinguished by a CTL* formula, to become indistinguishable by any CTL formula. We also define another weaker equivalence that is the weakest equivalence preserving CTL interpreted on the fair paths. As a consequence of our proof, we also obtain characterizations of states in the fair structure in terms of CTL* and CTL formulae.
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