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

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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. © 2006 Elsevier B.V. All rights reserved.

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Bollig, B., Waack, S., & Woelfel, P. (2006). Parity graph-driven read-once branching programs and an exponential lower bound for integer multiplication. Theoretical Computer Science, 362(1–3), 86–99. https://doi.org/10.1016/j.tcs.2006.05.035

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