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

Beate Bollig, Philipp Woelfel
2002 Lecture Notes in Computer Science  
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 ωnondeterministic communication complexity (for the nondeterministic acceptance modes ω ∈ {∨, ∧, ⊕}). We apply the technique in order to prove an exponential lower bound for integer multiplication for ωnondeterministic well-structured g.d.-BP1s.
more » ... (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 fnction which can be represented by polynomial size ω-nondeterministic BP1s that it has exponential complexity in the ωnondeterministic well-structured g.d.-BP1 model for ω ∈ {∨, ⊕}. This answers an open question from Brosenne, Homeister, and Waack [7], whether the nondeterministic BP1 model is in fact more powerful than the well-structured graph-driven variant.
doi:10.1007/3-540-45687-2_10 fatcat:ehj7iq2iy5euhe66rk2xvf4zz4