Equivalence between RCGS and CGS Clause Samples

Equivalence between RCGS and CGS. The only impact of using RCGS as opposed to CGS is increased efficiency of model checking, and better scaling as the number of agents increase. We argue for the claim about efficiency in the next section. In this section we show that this is the only change, i.e., that the the formulas valid on RCGS models are exactly the same as the formulas valid on CGS models. One way is obvious. For every CGS model, there is a corresponding RCGS model satisfying exactly the same formulas. To see this, we construct an RCGS with iden- tical state-space in which every agent is assigned to her own role. In every state the agents in that role (there is always exactly one) has the same actions available as the corresponding agent in the original model. The other direction requires a more technical argument. We do this by first giving a surjective function f that takes an RCGS and returns a CGS. Then we show that S and f (S) satisfy the same ATL formulas.
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