On learning bounded-width branching programs
Funda Ergün, S. Ravi Kumar, Ronitt Rubinfeld · 1995
In this paper, we study PAC-leaming algorithms for specialized classes of deterministic finite automata (DFA).Inpartictdar, we study branchingprogrsms, and we investigate the intluence of the width of the branching program on the difficulty of the learning problem.We first present a distribution-free algorithm for learning width-2 branching programs.We also give an algorithm for the proper learning of width-2 branching programs under uniform distribution on labeled samples.We then show that the existence of an efficient algorithm for learning width-3 branching programs would imply the existence of an efficient algorithm for learning DNF, which is not known to be the case.Fimlly, we show that the existence of an algorithm for learning width-3 branching programs would also yield an algorithm for learning a very restricted version of parity with noise.*This is more restrictive than the definition in [6], where the i-tb column depends on an arbitrary Zj and more than one column may depend on any particuk z,.