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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, October 16, 2007, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**Speaker**: Dominik Scheder

When thinking about complexity of decision problems, we are used to focus on time complexity. In this talk, I will state and prove two classical results of complexity theory relating to space, Savitch's Theorem and the Immerman-Szelepcsenyi Theorem. Despite being well-known theorems, their beautiful and surprising proofs are not as widely known as they are for other results in this area (Cook's Theorem stating that SAT is NP-complete, for instance).

Both theorems can be stated as results on how much space we need to solve the innocent reachability problem in directed graphs. Sloppily spoken, Savitch's Theorem implies that with respect to space complexity, nondeterminism is not much more powerful than determinism. Note that stark contrast to time complexity, where P e NP is widely believed to be true.

The Immeran-Szelepcsenyi Theorem implies that (most) nondeterministic space classes are closed under complement, i.e., NSPACE(...) = coNSPACE(...) (for decent "..."). Again, this is in contrast to time complexity, where most of us believe that NP e coNP.

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