Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, May 31, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Trinh Huynh

The Communication Complexity and Block Sensitivity of Search Problems

Given an input domain I and an output domain Z, a search problem defines for every input i in I a subset of Z to be the valid outputs for i. In a two-player communication search problem with input domains X and Y and output domain Z, Alice is given an input x in X, Bob is given an input y in Y, and they need to communicate to find a valid output in Z for their joint input (x,y). Motivation for studying the communication complexity of search problems comes from their applications to circuit depth lower bounds, to rank and tree-like size lower bounds in propositional proof complexity, and as we observed, also to length-space tradeoffs in proof complexity.

In this talk, I will describe our new analysis technique to lower bound the communication complexity of a broad class of communication search problems in terms of the critical block-sensitivity of search problems, a new notion we introduced that generalizes the block sensitivity of functions. This new technique enables us to obtain the first strong length-space tradeoffs in the so-called Cutting Planes and Polynomial Calculus Resolution proof systems for refuting constant-width CNF formulas.

This is based on joint work with Jakob Nordstrom (KTH Stockholm).

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