An Improved Hierarchy Result for Partitioned BDDs

Abstract.

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 / log log 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((n/ log^1+ε n) ^1/4 ) , where ε > 0 is an arbitrary small constant.