Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circuit equivalence in 2-nilpotent algebras   The circuit equivalence problem of a finite algebra $\mathbf A$ is the
computational problem of deciding whether two circuits over $\mathbf A$ define
the same function or not. This problem not just generalises the equivalence
problem for Boolean circuits, but is also of high interest in universal
algebra, as it models the problems of checking identities in $\mathbf A$. In
this paper we discuss the complexity for algebras from congruence modular
varieties. A partial classification was already given by Idziak and
Krzaczkowski, leaving essentially only a gap for nilpotent but not
supernilpotent algebras. We start a systematic study of this open case, proving
that the circuit equivalence problem is in P for $2$-nilpotent such algebras.

14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con