The consistency dimension and distribution-dependent learning from queries

We prove a new combinatorial characterization of polynomial learnability from equiva lence queries and state some of its consequences relating the learnability of a class with the learnability via equivalence and membership queries of its subclasses obtained by restricting the instance space Then we propose and study two models of query learning in which there is a probability distribution on the instance space both as an applica tion of the tools developed from the combinatorial characterization and as models of independent interest Work supported in part by the EC through the Esprit Program EU BRA program under project ALCOM IT and the EC Working Group EP NeuroColt II and by the spanish DGES PB Koala and by the German Israeli Foundation for Scienti c Research and Development grant I