Computational Limits on Team Identification of Languages

A team of learning machines is a multiset of learning machines. A team is said to successfully identify a concept just in case each member of some nonempty subset, of predetermined size, of the team identifies the concept. Team identification of programs for computable functions from their graphs ha...

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Bibliographic Details
Published in:Information and computation Vol. 130; no. 1; pp. 19 - 60
Main Authors: Jain, Sanjay, Sharma, Arun
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 10.10.1996
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Automata. Abstract machines. Turing machines
Computer science; control theory; systems
Exact sciences and technology
Theoretical computing
Learning
Abstract machine
Probabilistic automaton
Computational complexity
Language identifier
Single machine
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:A team of learning machines is a multiset of learning machines. A team is said to successfully identify a concept just in case each member of some nonempty subset, of predetermined size, of the team identifies the concept. Team identification of programs for computable functions from their graphs has been investigated by Smith. Pitt showed that this notion is essentially equivalent to function identification by a single probabilistic machine. The present paper introduces, motivates, and studies the more difficult subject of team identification of grammars for languages from positive data. It is shown that an analog of Pitt's result about equivalence of team function identification and probabilistic function identification does not hold for language identification, and the results in the present paper reveal a very complex structure for team language identification. It is also shown that for certain cases probabilistic language identification is strictly more powerful than team language identification. Proofs of many results in the present paper involve very sophisticated diagonalization arguments. Two very general tools are presented that yield proofs of new results from simple arithmetic manipulation of the parameters of known ones.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.1996.0081