ECCC-Report TR10-062https://eccc.weizmann.ac.il/report/2010/062Comments and Revisions published for TR10-062en-usSun, 11 Apr 2010 00:23:11 +0300
Paper TR10-062
| Logspace Versions of the Theorems of Bodlaender and Courcelle |
Michael Elberfeld,
Andreas Jakoby,
Till Tantau
https://eccc.weizmann.ac.il/report/2010/062Bodlaender'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.Sun, 11 Apr 2010 00:23:11 +0300https://eccc.weizmann.ac.il/report/2010/062