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

Date and Time: Tuesday, October 19, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Dominik Scheder

Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses.

This talk is based on a recent paper by Holger Dell and Dieter van Melkebeek. The setup consists of two friends, called Dominik and Marek. Dominik is quite slow, Marek is brilliant and fast. Dominik holds a k-CNF formula and wants to decide whether it is satisfiable. He asks his friend Marek for help, but unfortunately Dominik is on vacation and cell phone minutes are expensive. He could tell Marek the complete k-CNF formula over the phone, which would take O(n^k) bits. The paper states that basically Dominik cannot do better. To be precise, if there is an epsilon such that Dominik and Marek can solve the problem with communicating at most O(n^{k-epsilon}) bits, the polynomial hierarchy would collapse.

The result is not limited to SAT, but has applications to kernelization and probabilistically checkable proofs.

Source: Holger Dell, Dieter van Melkebeek: Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses, STOC 2010

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