Parity graph-driven read-once branching programs and an exponential lower bound for integer multiplication

Authors:
Beate Bollig;Stephan Waack;Philipp Woelfel
Affiliations:
FB Informatik, Univ. Dortmund, Dortmund, Germany;Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, Göttingen, Germany;FB Informatik, Univ. Dortmund, Dortmund, Germany and Department of Computer Science, University of Toronto, Toronto, Ont., Canada
Venue:
Theoretical Computer Science
Year:
2006

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Abstract

Branching programs are a well-established computation model for Boolean functions, especially read-once branching programs have been studied intensively. Exponential lower bounds for read-once branching programs are known for a long time. On the other hand, the problem of proving superpolynomial lower bounds for parity read-once branching programs is still open. In this paper restricted parity read-once branching programs are considered and an exponential lower bound on the size of the so-called well-structured parity graph-driven read-once branching programs for integer multiplication is proven. This is the first strongly exponential lower bound on the size of a parity nonoblivious read-once branching program model for an explicitly defined Boolean function. In addition, more insight into the structure of integer multiplication is yielded.