Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

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

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Trinh Huynh

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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