Functions computable by Boolean circuits of logarithmic depth and branching programs of a special type

D. M. Barrington proved the coincidence of the class NC¹ of functions computable by the circuits of logarithmic depth with the class of functions computable by branching programs of constant width and polynomial length (BWBP). In this paper, the structure of branching programs suggested by the Barrington method is defined more exactly. Namely, it is proved that we can compute all functions from NC¹ and only them by the k-OBDDs of polynomial size and width 5. This can be reformulated as poly(n)-OBDD₅ =NC¹.