Abstract. We present several results on comparative complexity for different variants of OBDD models.-We present some results on comparative complexity of classical and quantum OBDDs. We consider a partial function depending on parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2 but any classical OBDD (deterministic or stable bounded error probabilistic) needs width 2 k+1 . -We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient than classical one. In particular, an explicit function is presented which is computed by a quantum nondeterministic OBDD with constant width but any classical nondeterministic OBDD for this function needs non-constant width. -We also present new hierarchies on widths of deterministic and nondeterministic OBDDs. We focus both on small and large widths.
In this paper we study a model of Quantum Branching Program (QBP) and investigate its computational power. We define several natural restrictions of a general QBP model, such as a read-once and a read-k-times QBP, noting that obliviousness is inherent in a quantum nature of such programs.In particular we show that any Boolean function can be computed deterministically (exactly) by a read-once QBP in width O(2 n ), contrary to the analogous situation for quantum finite automata. Further we display certain symmetric Boolean function which is computable by a read-once QBP with O(log n) width, which requires a width Ω(n) on any deterministic read-once BP and (classical) randomized read-once BP with permanent transitions at each level.We present a general lower bound for the width of read-once QBPs, showing that the upper bound for a considered symmetric function is almost tight.
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