PP-2018-10: Finite identification with positive and with complete data

PP-2018-10: de Jongh, Dick and Vargas, Ana Lucia (2018) Finite identification with positive and with complete data. [Pre-print]

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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
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

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