Department Colloquium

Department of Mathematics
Princeton University


February 9th, 2000

Turning questions into games

There are intimate connections between classes of questions and classes of games. For example, suppose we have some question whose answer, either "yes" or "no", can be determined using a small amount of memory (but possibly a lot of time). A classic result says that we can efficiently transform this question into a two-player game such that:
1) Each player makes a small number of short moves,
2) The winner is easy to determine and
3) The first player has a (possibly quite difficult) winning strategy if and only if the answer to the original question is "yes".
We survey a number of results of this type, and discuss our work with Uri Feige on how to convert long chess games into short poker games.