Near-Optimal Lower Bounds on Quantifier Depth and Weisfeiler - Leman Refinement Steps
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
We prove near-optimal trade-offs for quantifier depth versus number of variables in first-order logic by exhibiting pairs of n-element structures that can be distinguished by a k-variable first-order sentence but where every such sentence requires quantifier depth at least n (k= log k). Our trade-offs also apply to first-order counting logic, and by the known connection to the k-dimensional Weisfeiler-Leman algorithm imply near-optimal lower bounds on the number of refinement iterations. A key component in our proof is the hardness condensation technique recently introduced by [Razborov '16] in the context of proof complexity. We apply this method to reduce the domain size of relational structures while maintaining the quantifier depth required to distinguish them.
Originalsprog | Engelsk |
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Titel | Proceedings of the 31st Annual ACM-IEEE Symposium on Logic in Computer Science, LICS 2016 |
Antal sider | 10 |
Forlag | Institute of Electrical and Electronics Engineers Inc. |
Publikationsdato | 5 jul. 2016 |
Sider | 267-276 |
ISBN (Elektronisk) | 9781450343916 |
DOI | |
Status | Udgivet - 5 jul. 2016 |
Eksternt udgivet | Ja |
Begivenhed | 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016 - New York, USA Varighed: 5 jul. 2016 → 8 jul. 2016 |
Konference
Konference | 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016 |
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Land | USA |
By | New York |
Periode | 05/07/2016 → 08/07/2016 |
Sponsor | ACM Special Interest Group on Logic and Computation (SIGLOG), Association for Computing Machinery, et al., European Association for Computer Science Logic, IEEE Computer Society, IEEE Technical Committee on Mathematical Foundations of Computer Science |
Navn | Proceedings - Symposium on Logic in Computer Science |
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Vol/bind | 05-08-July-2016 |
ISSN | 1043-6871 |
ID: 251868527