A Lower Bound Technique for Nondeterministic Graph-Driven Read-Once-Branching Programs and Its Applications

Abstract

We present a new lower bound technique for a restricted branching program model, namely for nondeterministic graph-driven read-once branching programs (g.d.-BP1s). The technique is derived by drawing a connection between ω-nondeterministic g.d.-BP1s and ω-nondeterministic communication complexity (for the nondeterministic acceptance modes ω∈{⋁,⋀,⊕}). We apply the technique in order to prove an exponential lower bound for integer multiplication for ω-nondeterministic well-structured g.d.-BP1s. (For ω=⊕ an exponential lower bound was already obtained in [5] by using a different technique.) Further, we use the lower bound technique to prove for an explicitly defined function which can be represented by polynomial size ω-nondeterministic BP1s that it has exponential complexity in the ω-nondeterministic well-structured g.d.-BP1 model for ω∈{⋁,⊕}. This answers an open question from Brosenne et al., whether the nondeterministic BP1 model is in fact more powerful than the well-structured graph-driven variant.