Descriptive Complexity of Finite Structures: Saving the Quantifier Rank
| dc.creator | Pikhurko, Oleg | |
| dc.creator | Verbitsky, Oleg | |
| dc.date | 2003-05-16 | |
| dc.date | 2003-11-05 | |
| dc.date.accessioned | 2026-07-07T04:58:05Z | |
| dc.date.available | 2026-07-07T04:58:05Z | |
| dc.description | Given a relational structure M on n elements, let D(M) be the minimum quantifier rank of a first order formula identifying M up to isomorphism in the class of n-element structures. The obvious upper bound is D(M)\le n. We show that if the relations in M have arity at most k, then D(M)<(1-\frac{1}{2k})n+k^2-k+2. The coefficient at n, which equals 1-\frac{1}{2k}, is probably not best possible but this is the first known bound having it strictly below 1 (for fixed k). If one is content to have the worse coefficient 1-\frac{1}{2k^2+2}, then one can choose an identifying formula of a very special form: a prenex formula with at most one quantifier alternation. A few other results in this vein are presented. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305244 | |
| dc.identifier | http://arxiv.org/abs/math/0305244 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67491 | |
| dc.subject | Logic | |
| dc.subject | Combinatorics | |
| dc.subject | 03B70, 03B80, 05C60, 08A02 | |
| dc.title | Descriptive Complexity of Finite Structures: Saving the Quantifier Rank | |
| dc.type | text |