On the power of algebraic branching programs of width two

Authors:
Eric Allender;Fengming Wang
Affiliations:
Department of Computer Science, Rutgers University, Piscataway, NJ;Department of Computer Science, Rutgers University, Piscataway, NJ
Venue:
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Year:
2011

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Abstract

We show that there are families of polynomials having small depthtwo arithmetic circuits that cannot be expressed by algebraic branching programs of width two. This clarifies the complexity of the problem of computing the product of a sequence of two-by-two matrices, which arises in several settings.