Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random 3CNF formulas elude the Lovasz theta function   Let $\phi$ be a 3CNF formula with n variables and m clauses. A simple
nonconstructive argument shows that when m is sufficiently large compared to n,
most 3CNF formulas are not satisfiable. It is an open question whether there is
an efficient refutation algorithm that for most such formulas proves that they
are not satisfiable. A possible approach to refute a formula $\phi$ is: first,
translate it into a graph $G_{\phi}$ using a generic reduction from 3-SAT to
max-IS, then bound the maximum independent set of $G_{\phi}$ using the Lovasz
$\vartheta$ function. If the $\vartheta$ function returns a value $< m$, this
is a certificate for the unsatisfiability of $\phi$. We show that for random
formulas with $m < n^{3/2 -o(1)}$ clauses, the above approach fails, i.e. the
$\vartheta$ function is likely to return a value of m.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga