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Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs

Author Berit Grußien

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Berit Grußien

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Berit Grußien. Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CSL.2017.26

Abstract

We show that the class of chordal claw-free graphs admits LREC=-definable canonization. LREC= is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm for the class of chordal claw-free graphs, and that LREC= captures logarithmic space on this graph class. Since LREC= is contained in fixed-point logic with counting, we also obtain that fixed-point logic with counting captures polynomial time on the class of chordal claw-free graphs.
Keywords
  • Descriptive complexity
  • logarithmic space
  • polynomial time
  • chordal claw-free graphs

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