Complexity of decision trees for boolean functions

For every positive integer k we present an example of a Boolean function f(k): of n = ((2k)(k)) + 2k variables, an optimal deterministic tree T-k' for f(k) of complexity 2k + 1 as well as a nondeterministic decision tree T-k computing f(k) with complexity k + 2; thus of complexity about 1/2 of the optimal deterministic decision tree. Certain leaves of T-k are called priority leaves. For every input a is an element of {0, 1}(n) if any of the parallel computation reaches a priority leaves then its label is f(k) (a). If the priority leaves are not reached at all then the label on any of the remaining leaves reached by the computation is f(k) (a).