Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Separating ABPs and Some Structured Formulas in the Non-Commutative
  Setting   The motivating question for this work is a long standing open problem, posed
by Nisan (1991), regarding the relative powers of algebraic branching programs
(ABPs) and formulas in the non-commutative setting. Even though the general
question continues to remain open, we make some progress towards its
resolution. To that effect, we generalise the notion of ordered polynomials in
the non-commutative setting (defined by \Hrubes, Wigderson and Yehudayoff
(2011)) to define abecedarian polynomials and models that naturally compute
them.
  Our main contribution is a possible new approach towards separating formulas
and ABPs in the non-commutative setting, via lower bounds against abecedarian
formulas. In particular, we show the following.
  There is an explicit n-variate degree d abecedarian polynomial $f_{n,d}(x)$
such that 1. $f_{n, d}(x)$ can be computed by an abecedarian ABP of size O(nd);
2. any abecedarian formula computing $f_{n, \log n}(x)$ must have size that is
super-polynomial in n.
  We also show that a super-polynomial lower bound against abecedarian formulas
for $f_{\log n, n}(x)$ would separate the powers of formulas and ABPs in the
non-commutative setting.

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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio