Sharpening Occam's razor

We provide a new representation-independent formulation of Occam's razor theorem, based on Kolmogorov complexity. This new formulation allows us to: (i) obtain better sample complexity than both length-based [Blumer et al., Inform. Process. Lett. 24 (1987) 377-380] and VC-based [Blumer et al., J. ACM 35 (1989) 929-965] versions of Occam's razor theorem, in many applications; and (ii) achieve a sharper reverse of Occam's razor theorem than that of Board and Pitt [STOC, 1999, pp. 54-63]. Specifically, we weaken the assumptions made by Board and Pitt [STOC, 1999, pp. 54-63] and extend the reverse to superpolynomial running times. (C) 2002 Elsevier Science B.V. All rights reserved.