Learning of monotone functions with single error correction

Learning of monotone functions is a well-known problem. Results obtained by V. K. Korobkov and G. Hansel imply that the complexity ) of learning of monotone Boolean functions equals + ( ) denotes the least number of queries on the value of an unknown monotone function on a given input sufficient to...

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Bibliographic Details
Published inDiscrete mathematics and applications Vol. 31; no. 3; pp. 193 - 205
Main Authors Selezneva, Svetlana N., Liu, Yu
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 25.06.2021
Walter de Gruyter GmbH
Subjects
Algorithms
Boolean
Boolean algebra
Boolean function
Boolean functions
chain
chain partition
Codes
Complexity
dimensional Boolean cube
error
Error correction
Error correction & detection
Hansel chains
Learning
learning complexity
learning of functions
Linear programming
monotone function
Monotone functions
Queries
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Summary:Learning of monotone functions is a well-known problem. Results obtained by V. K. Korobkov and G. Hansel imply that the complexity ) of learning of monotone Boolean functions equals + ( ) denotes the least number of queries on the value of an unknown monotone function on a given input sufficient to identify an arbitrary -ary monotone function). In our paper we consider learning of monotone functions in the case when the teacher is allowed to return an incorrect response to at most one query on the value of an unknown function so that it is still possible to correctly identify the function. We show that learning complexity in case of the possibility of a single error is equal to the complexity in the situation when all responses are correct.
ISSN:0924-9265
1569-3929
DOI:10.1515/dma-2020-0017