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### Paper:

TR10-062 | 7th April 2010 14:01

#### Logspace Versions of the Theorems of Bodlaender and Courcelle

TR10-062
Authors: Michael Elberfeld, Andreas Jakoby, Till Tantau
Publication: 11th April 2010 00:23
Bodlaender's Theorem states that for every $k$ there is a linear-time algorithm that decides whether an input graph has tree width~$k$ and, if so, computes a width-$k$ tree composition. Courcelle's Theorem builds on Bodlaender's Theorem and states that for every monadic second-order formula $\phi$ and for
every $k$ there is a linear-time algorithm that decides whether a given logical structure $\mathcal A$ of tree width at most $k$ satisfies $\phi$. We prove that both theorems still hold when linear time'' is replaced by logarithmic space.'' The transfer of the powerful theoretical framework of monadic second-order logic and bounded tree width to logarithmic space allows us to settle a number of both old and recent open problems in the logspace world.