On the Power of Imperfect Information

Dietmar Berwanger & Laurent Doyen
We present a polynomial-time reduction from parity games with imperfect information to safety games with imperfect information. Similar reductions for games with perfect information typically increase the game size exponentially. Our construction avoids such a blow-up by using imperfect information to realise succinct counters which cover a range exponentially larger than their size. In particular, the reduction shows that the problem of solving imperfect-information games with safety conditions is \EXPTIME-complete.