Catalytic Branching Programs from Groups and General Protocols
Article No.: 5, Pages 1 - 17
Abstract
CCCatalytic branching programs (catalytic bps) compute the same n-bit Boolean function f at multiple entry points that need to be remembered at the exit nodes of the branching program (bp). When a doubly exponential number of entry points is allowed, linear amortized catalytic bp size is known to be achievable for any f. Here a method is introduced that produces a catalytic bp out of a reversible bp and a deterministic dag-like communication protocol. In a multiplicity range as low as linear, approximating a threshold is shown possible at linear amortized cost. In the same low range, computing Maj and Mod are shown possible at a cost that beats the brute force repetition of the best known bp for these functions by a polylog factor. In the exponential range, the method yields O(n log n) amortized cost for any symmetric function.
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December 2023
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Association for Computing Machinery
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Publication History
Published: 12 December 2023
Online AM: 17 May 2023
Accepted: 01 February 2023
Received: 28 September 2019
Published in TOCT Volume 15, Issue 3-4
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