Basis Collapse in Holographic Algorithms

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Jin-yi Cai, Pinyan Lu

Published: 2008, Last Modified: 09 Jan 2026Comput. Complex. 2008EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Holographic algorithms are a novel approach to design polynomial time computations using linear superpositions. Most holographic algorithms are designed with basis vectors of dimension 2. Recently Valiant showed that a basis of dimension 4 can be used to solve in P an interesting (restrictive SAT) counting problem mod 7. This problem without modulo 7 is #P-complete, and counting mod 2 is NP-hard.