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Revision #2 to TR15-204 | 23rd October 2017 14:44

#### Sums of read-once formulas: How many summands suffice?

Revision #2
Authors: Meena Mahajan, Anuj Tawari
Accepted on: 23rd October 2017 14:44
Keywords:

Abstract:

An arithmetic read-once formula (ROF) is a formula (circuit of fan-out
1) over
$+, \times$ where each variable labels at most one leaf.
Every multilinear polynomial can be expressed as the sum of ROFs.
In this work, we prove, for certain multilinear polynomials,
a tight lower bound on the number of summands in such an expression.

Changes to previous version:

Added an exponential lower bound over any field.

Revision #1 to TR15-204 | 11th March 2016 10:25

#### Sums of read-once formulas: How many summands suffice?

Revision #1
Authors: Meena Mahajan, Anuj Tawari
Accepted on: 11th March 2016 10:25
Keywords:

Abstract:

An arithmetic read-once formula (ROF) is a formula (circuit of fan-out
1) over
$+, \times$ where each variable labels at most one leaf.
Every multilinear polynomial can be expressed as the sum of ROFs.
In this work, we prove, for certain multilinear polynomials,
a tight lower bound on the number of summands in such an expression.

### Paper:

TR15-204 | 14th December 2015 08:33

#### Sums of read-once formulas: How many summands suffice?

TR15-204
Authors: Meena Mahajan, Anuj Tawari
Publication: 14th December 2015 09:59
Keywords:

Abstract:

An arithmetic read-once formula (ROF) is a formula (circuit of fan-out
1) over
$+, \times$ where each variable labels at most one leaf.
Every multilinear polynomial can be expressed as the sum of ROFs.
In this work, we prove, for certain multilinear polynomials,
a tight lower bound on the number of summands in such an expression.

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