English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

We study a probability distribution d on the truth assignments to a uniformbinary AND-OR tree. Liu and Tanaka [2007, Inform. Process. Lett.] showed thefollowing: If d achieves the equilibrium among independent distributions (ID)then d is an independent identical distribution (IID). We show a stronger formof the above result. Given a real number r such that 0 < r < 1, we consider aconstraint that the probability of the root node having the value 0 is r. Ourmain result is the following: When we restrict ourselves to IDs satisfying thisconstraint, the above result of Liu and Tanaka still holds. The proof employsclever tricks of induction. In particular, we show two fundamentalrelationships between expected cost and probability in an IID on an OR-ANDtree: (1) The ratio of the cost to the probability (of the root having thevalue 0) is a decreasing function of the probability x of the leaf. (2) Theratio of derivative of the cost to the derivative of the probability is adecreasing function of x, too.

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