Learnability of Kolmogorov-easy circuit expressions via queries

Abstract

Circuit expressions were introduced to provide a natural link between Computational Learning and certain aspects of Structural Complexity. Upper and lower bounds on the learnability of circuit expressions are known. We study here the case in which the circuit expressions are of low (time-bounded) Kolmogorov complexity. We show that these are polynomial-time learnable from membership queries in the presence of an NP oracle. We also exactly characterize, in terms of advice classes, the sets that have such easy circuit expressions, obtain consequences regarding their lowness, and precisely identify the subclass whose circuit expressions can be learned from membership queries alone, by means of doubly tally polynomial time degrees. The extension of the results to various Kolmogorov complexity bounds is discussed.