Lower Bounds for Syntactically Multilinear Algebraic Branching Programs

2008 ◽  
pp. 407-418 ◽  
Author(s):  
Maurice J. Jansen
Keyword(s):  
Lower Bounds ◽  
Branching Programs ◽  
Algebraic Branching Programs

scholarly journals Identity Testing and Lower Bounds for Read- k Oblivious Algebraic Branching Programs

2018 ◽  
Vol 10 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Matthew Anderson ◽  
Michael A. Forbes ◽  
Ramprasad Saptharishi ◽  
Amir Shpilka ◽  
Ben Lee Volk
Keyword(s):  
Lower Bounds ◽  
Branching Programs ◽  
Identity Testing ◽  
Algebraic Branching Programs

On Proving Parameterized Size Lower Bounds for Multilinear Algebraic Models

2020 ◽  
Vol 177 (1) ◽  
pp. 69-93
Author(s):  
Purnata Ghosal ◽  
B.V. Raghavendra Rao
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Partial Derivative ◽  
Computable Function ◽  
Arithmetic Circuits ◽  
Multilinear Polynomial ◽  
Algebraic Models ◽  
Branching Programs ◽  
Algebraic Branching Programs ◽  
Derivative Matrix

We consider the problem of obtaining parameterized lower bounds for the size of arithmetic circuits computing polynomials with the degree of the polynomial as the parameter. We consider the following special classes of multilinear algebraic branching programs: 1) Read Once Oblivious Branching Programs (ROABPs), 2) Strict interval branching programs, 3) Sum of read once formulas with restricted ordering. We obtain parameterized lower bounds (i.e., nΩ(t(k)) lower bound for some function t of k) on the size of the above models computing a multilinear polynomial that can be computed by a depth four circuit of size g(k)nO(1) for some computable function g. Further, we obtain a parameterized separation between ROABPs and read-2 ABPs. This is obtained by constructing a degree k polynomial that can be computed by a read-2 ABP of small size such that the rank of the partial derivative matrix under any partition of the variables is large.

scholarly journals Lower Bounds for Monotone Span Programs

1994 ◽  
Vol 1 (46) ◽  
Author(s):  
Amos Beimel
Keyword(s):  
Lower Bounds ◽  
Secret Sharing ◽  
Algebraic Model ◽  
New Technique ◽  
Secret Sharing Schemes ◽  
Branching Programs ◽  
Model Of Computation ◽  
Monotone Span Programs ◽  
Span Programs ◽  
A New Technique

The model of span programs is a linear algebraic model of computation. Lower bounds for span programs imply lower bounds for contact schemes, symmetric branching programs and for formula size. Monotone span programs correspond also to linear secret-sharing schemes. We present a new technique for proving lower bounds for monotone span programs. The main result proved here yields quadratic lower bounds for the size of monotone span programs, improving on the largest previously known bounds for explicit functions. The bound is asymptotically tight for the function corresponding to a class of 4-cliques.

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