Conflict complexity is lower bounded by block sensitivity

TL;DR

This paper establishes that the conflict complexity of any total Boolean function is at least half of its block sensitivity, linking two complexity measures and advancing understanding in decision tree complexity.

Contribution

It proves a lower bound on conflict complexity in terms of block sensitivity and explores its relation to certificate complexity.

Findings

Conflict complexity is at least half of block sensitivity for all total Boolean functions.

Comparison between conflict complexity and certificate complexity offers new insights.

Provides a foundational bound useful for decision tree complexity analysis.

Abstract

We show conflict complexity of every total Boolean function, recently introduced in [Swagato Sanyal. A composition theorem via conict complexity. arXiv preprint arXiv:1801.03285, 2018.] to prove a composition theorem of randomized decision tree complexity, is at least a half of its block sensitivity. We propose to compare conflict complexity with certificate complexity, and explain why it could be interesting.