Date & Time: December 4th (Thu) 14:00- 15:00
Place: CELC 4F Seminar room
Toshio Suzuki
Tokyo Metropolitan University

*Title:
Equilibrium Points of an AND-OR Tree: under Constraints on Probability

*Abstract:
We study a probability distribution $d$ on the truth assignments to a
uniform binary AND-OR tree. Liu and Tanaka [2007, Inform. Process.
Lett.] showed the following: If $d$ achieves the equilibrium among
independent distributions (ID) then $d$ is an independent identical
distribution (IID).

We show a stronger form of the above result. Given a real number $r$
such that $0 < r < 1$, we consider a constraint that the probability
of the root node having the value 0 is $r$. Our main result is the
following: When we restrict ourselves to IDs satisfying this
constraint, the above result of Liu and Tanaka still holds.

Keys to the solution are two fundamental relationships between
expected cost and probability in an IID on an OR-AND tree.

(1) The ratio of the cost to the probability (of the root having the
value 0) is a decreasing function of the probability $x$ of the leaf.

(2) The ratio of derivative of the cost to the derivative of the
probability is decreasing function of $x$, too.

This work is a collaboration with Yoshinao Niida. Our research is
partially supported by KAKENHI (C) 22540146 and (B) 23340020.

Preprint arXiv:1401.8175

END OF TALK INFO.