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

Authors:
Beate Bollig;Philipp Woelfel
Affiliations:
FB Informatik, LS2, University of Dortmund, 44221 Dortmund, Germany;FB Informatik, LS2, University of Dortmund, 44221 Dortmund, Germany
Venue:
Theory of Computing Systems
Year:
2005

Citing 0
Cited 2

On the OBDD complexity of the most significant bit of integer multiplication

TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
On the OBDD complexity of the most significant bit of integer multiplication

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

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.