Computational Aspects of Parallel Attribute-Efficient Learning

Abstract

We address the problem of nonadaptive learning of Boolean functions with few relevant variables by membership queries. In another recent paper [7] we have characterized those assignment families (query sets) which are sufficient for nonadaptive learning of this function class, and we studied the query number. However, the reconstruction of the given Boolean function from the obtained responses is an important matter as well in applying such nonadaptive strategies. The computational amount for this is apparently too high if we use our query families in a straightforward way. Therefore we introduce algorithms where also the computational complexity is reasonable, rather than the query number only. The idea is to apply our assignment families to certain coarsenings of the given Boolean function, followed by simple search and verification routines.