Uniqueness of optimal randomized algorithms for balanced AND-OR trees

Abstract

In this paper, we investigate optimal randomized algorithms of balanced AND-OR tree evaluation, with regards to query complexity. For balanced AND-OR trees, previous studies have made a good progress on the uniqueness of eigen-distributions, i.e., optimal mixed strategies determining an input (Suzuki & Nakamura 2012, Peng et. al. 2016). However, it has been considered that the dual problem, the uniqueness of optimal randomized algorithms, is rather difficult, and a new approach has been needed. By introducing a group-theoretical methods, we show that the uniqueness does not hold and there are uncountably many optimal randomized algorithms.