Monotone Depth Lower Bounds using Communication Complexity

Speaker:
Sreejata Kishor Bhattacharya
Organiser:
Varun Ramanathan
Date:
Friday, 25 Aug 2023, 16:00 to 17:00
Venue:
A-201
Abstract
We shall show that any monotone circuit (with fan-in 2) which determines if a graph has a perfect matching must have depth Ω(n). This shows that efficient deterministic parallel algorithms for the perfect matching problem must use negation. To do so, we shall use tools from communication complexity: more specifically, we shall show that such a circuit will imply a low-cost communication protocol for set-disjointness, which is known to be hard.