Near-Optimal Lower Bounds on Quantifier Depth and Weisfeiler - Leman Refinement Steps
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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.
Original language | English |
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Title of host publication | Proceedings of the 31st Annual ACM-IEEE Symposium on Logic in Computer Science, LICS 2016 |
Number of pages | 10 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Publication date | 5 Jul 2016 |
Pages | 267-276 |
ISBN (Electronic) | 9781450343916 |
DOIs | |
Publication status | Published - 5 Jul 2016 |
Externally published | Yes |
Event | 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016 - New York, United States Duration: 5 Jul 2016 → 8 Jul 2016 |
Conference
Conference | 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016 |
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Land | United States |
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 |
Series | Proceedings - Symposium on Logic in Computer Science |
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Volume | 05-08-July-2016 |
ISSN | 1043-6871 |
- bounded variable fragment, first-order counting logic, First-order logic, hardness condensation, lower bounds, quantifier depth, refinement iterations, trade-offs, Weisfeiler - Leman, XORification
Research areas
ID: 251868527