PP-2018-10: de Jongh, Dick and Vargas, Ana Lucia (2018) Finite identification with positive and with complete data. [Pre-print]
Preview |
Text
Tbilisi-Proceedings-FULLcorrected.pdf Download (334kB) | Preview |
Abstract
We study the differences between finite identifiability of re- cursive languages with positive and with complete data. In finite families the difference lies exactly in the fact that for positive identification the families need to be anti-chains, while in in the infinite case it is less sim- ple, being an anti-chain is no longer a sufficent condition. We also show that with complete data there are no maximal learnable families whereas with positive data there usually are, but there do exist positively identifi- able familes without a maximal positively identifiable extension. We also investigate a conjecture of ours, namely that each positively identifiable family has either finitely many or continuously many maximal noneffec- tively positively identifiable extensions. We verify this conjecture for the restricted case of families of equinumerous finite languages.
| Item Type: | Pre-print |
|---|---|
| Report Nr: | PP-2018-10 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2018 |
| Uncontrolled Keywords: | formal learning theory, finite identification, positive data, complete data, indexed family, anti-chains |
| Subjects: | Computation Mathematics |
| Depositing User: | Prof. Dick de Jongh |
| Date Deposited: | 27 May 2018 17:39 |
| Last Modified: | 27 May 2018 17:39 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1609 |
Actions (login required)
 |
View Item |
