Simulating Logspace-Recursion with Logarithmic Quantifier Depth

The fixed-point logic LREC= was developed by Grohe et al. (CSL 2012) in the quest for a logic to capture all problems decidable in logarithmic space. It extends FO+C, first-order logic with counting, by an operator that formalises a limited form of recursion. We show that for every LREC=-definable property on relational structures, there is a constant k such that the k-variable fragment of first-order logic with counting quantifiers expresses the property via formulae of logarithmic quantifier depth. This yields that any pair of graphs separable by the property can be distinguished with the k-dimensional Weisfeiler-Leman algorithm in a logarithmic number of iterations. In particular, it implies that the algorithm identifies every interval graph and every chordal claw-free graph in logarithmically many iterations. Joint work with Steffen van Bergerem, Martin Grohe, and Sandra Kiefer Contributed talk given by Luca Oeljeklaus

Authors

• Luca Oeljeklaus

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