Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gadgets and Anti-Gadgets Leading to a Complexity Dichotomy   We introduce an idea called anti-gadgets in complexity reductions. These
combinatorial gadgets have the effect of erasing the presence of some other
graph fragment, as if we had managed to include a negative copy of a graph
gadget. We use this idea to prove a complexity dichotomy theorem for the
partition function $Z(G)$ on 3-regular directed graphs $G$, where each edge is
given a complex-valued binary function $f: \{0,1\}^2 \rightarrow \mathbb{C}$.
We show that \[Z(G) = \sum_{\sigma: V(G) \to \{0,1\}} \prod_{(u,v) \in E(G)}
f(\sigma(u), \sigma(v)),\] is either computable in polynomial time or #P-hard,
depending explicitly on $f$.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con