| Autor: |
van Bergerem, Steffen, Grohe, Martin, Kiefer, Sandra, Oeljeklaus, Luca |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
The fixed-point logic LREC= was developed by Grohe et al. (CSL 2011) 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 a constant dimension of the algorithm identifies every interval graph and every chordal claw-free graph in logarithmically many iterations, since every such graph admits LREC=-definable canonisation. |
| Databáze: |
arXiv |
| Externí odkaz: |
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