Width Hierarchy for k-OBDD of Small Width

In this paper was explored well known model k-OBDD. There are proven width based hierarchy of classes of boolean functions which computed by k-OBDD. The proof of hierarchy is based on sufficient condition of Boolean function's non representation as k-OBDD and complexity properties of Boolean function SAF. This function is modification of known Pointer Jumping (PJ) and Indirect Storage Access (ISA) functions.Comment: 8 page

An Improved Hierarchy Result for Partitioned BDDs

One of the great challenges of complexity theory is the problem of analyzing the dependence of the complexity of Boolean functions on the resources nondeterminism and randomness. So far, this problem could be solved only for very few models of computation. For so-called partitioned binary decision diagrams, which are a restricted variant of nondeterministic read-once branching programs, Bollig and Wegener have proven an astonishing hierarchy result which shows that the smallest possible decrease of the available amount of nondeterminism may incur an exponential blow-up of the branching program size. They have shown that k-partitioned BDDs which may nondeterministically choose between k alternative subprograms may be exponentially larger than (k + 1)-partitioned BDDs for the same function if k = o # (log n/ loglog n) 1/2 # , where n is the input size. In this paper, an improved hierarchy result is established which still works if the number of nondeterministic decisions is O ..