Learning of monotone functions with single error correction

Abstract

Abstract Learning of monotone functions is a well-known problem. Results obtained by V. K. Korobkov and G. Hansel imply that the complexity φM(n) of learning of monotone Boolean functions equals Cn⌊n/2⌋ $\begin{array}{} \displaystyle C_n^{\lfloor n/2\rfloor} \end{array}$ + Cn⌊n/2⌋+1 $\begin{array}{} \displaystyle C_n^{\lfloor n/2\rfloor+1} \end{array}$ (φM(n) denotes the least number of queries on the value of an unknown monotone function on a given input sufficient to identify an arbitrary n-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.