Unexpected Upper Bounds on the Complexity of Some Communication Games

The results that we have presented should serve a as a warning: reducing a problem in complexity theory to a communication game may be only a first small step towards the solution, however intuitively clear the game may look like. Still, if we do not look just for record lower bounds, these reductions may often be, in a sense, very rewarding, as they lead to nice mathematical problems and show connections with other branches of mathematics.

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