The Dynamic Descriptive Complexity of k-Clique
Logic in Computer Science
2016-10-31 v1
Abstract
In this work the dynamic descriptive complexity of the k-clique query is studied. It is shown that when edges may only be inserted then k-clique can be maintained by a quantifier-free update program of arity k-1, but it cannot be maintained by a quantifier-free update program of arity k-2 (even in the presence of unary auxiliary functions). This establishes an arity hierarchy for graph queries for quantifier-free update programs under insertions. The proof of the lower bound uses upper and lower bounds for Ramsey numbers.
Cite
@article{arxiv.1610.09089,
title = {The Dynamic Descriptive Complexity of k-Clique},
author = {Thomas Zeume},
journal= {arXiv preprint arXiv:1610.09089},
year = {2016}
}
Comments
An extended abstract of this work appeared in the proceedings of the conference Mathematical Foundations of Computer Science 2014 (MFCS 2014)