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Logspace Versions of the Theorems of Bodlaender and Courcelle

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3 Author(s)
Michael Elberfeld ; Inst. fur Theor. Inf., Univ. zu Lubeck, Lübeck, Germany ; Andreas Jakoby ; Till Tantau

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 φ and for every k there is a linear-time algorithm that decides whether a given logical structure A of tree width at most k satisfies φ. 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 log space world.

Published in:

Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on

Date of Conference:

23-26 Oct. 2010