Recursion theoretic characterizations of language learning:

Abstract: "An attempt is made to build 'bridges' between machine language learning and recursive function theory. Formal language learning classes are characterized in terms of recursion theoretic notions like standardizing operations and recursively enumerable classes. Connections be...

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Hauptverfasser: Jain, Sanjay (VerfasserIn), Sharma, Arun (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Rochester, NY 1989
Schriftenreihe:University of Rochester <Rochester, NY> / Department of Computer Science: Technical report 281
Schlagworte:
Zusammenfassung:Abstract: "An attempt is made to build 'bridges' between machine language learning and recursive function theory. Formal language learning classes are characterized in terms of recursion theoretic notions like standardizing operations and recursively enumerable classes. Connections between Gold's seminal notion of identification, referred to as TxtEx-identification, and standardizing operations are investigated. It is shown that the class of languages that can be TxtEx-identified is properly contained in the class of languages that are limit-effectively standardizable. A restricted form of standardizability, which has the same power as TxtEx-identification, is presented
The notion of TxtEx-identification is relaxed (by providing additional information about the language being learned), so that the classes of languages that can be identified by this new criterion are exactly the same as the classes of languages that are limit-effectively standardizable. A connection between the above criteria and r.e. class of languages is also investigated. It is shown that for the class of languages identified by the above criteria, there exists a computable numbering that has exactly one index for infinite languages in the class and a finite number of indices for the finite languages in the class. Motivation for these characterizations are derived from the work of Freivald's, Kinber, and Wiehagen on the inference of programs for recursive functions from their graphs
However, new notions have to be invented to characterize language learning, and proofs are considerably more difficult.
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