Competitive Boolean Function Evaluation: Beyond Monotonicity, and the Symmetric Case

TL;DR

This paper investigates the limits of competitive ratios in Boolean function evaluation beyond monotone functions, providing bounds and exact characterizations for symmetric functions with a simple polynomial-time algorithm.

Contribution

It introduces the first non-trivial bounds for non-monotone Boolean functions and precisely characterizes the optimal competitiveness for symmetric functions.

Findings

Established bounds for non-monotone Boolean functions

Exact competitiveness characterization for symmetric functions

Developed a polynomial-time algorithm for evaluation

Abstract

We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the particular case of symmetric functions our bounds are matching and we exactly characterize the best possible competitiveness achievable by a deterministic algorithm. Our upper bound is obtained by a simple polynomial time algorithm.