Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The birth of the contradictory component in random 2-SAT   We prove that, with high probability, the contradictory components of a
random 2-SAT formula in the subcritical phase of the phase transition have only
3-regular kernels. This follows from the relation between these kernels and the
complex component of a random graph in the subcritical phase. This partly
settles the question about the structural similarity between the phase
transitions in 2-SAT and random graphs. As a byproduct, we describe the
technique that allows to obtain a full asymptotic expansion of the
satisfiability in the subcritical phase. We also obtain the distribution of the
number of contradictory variables and the structure of the spine in the
subcritical phase.

25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph