### Revision(s):

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Revision #2 to TR15-204 | 23rd October 2017 14:44
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#### Sums of read-once formulas: How many summands suffice?

**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.

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Revision #1 to TR15-204 | 11th March 2016 10:25
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#### Sums of read-once formulas: How many summands suffice?

**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:

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TR15-204 | 14th December 2015 08:33
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#### Sums of read-once formulas: How many summands suffice?

**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.