Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A high-performance analog Max-SAT solver and its application to Ramsey
  numbers   We introduce a continuous-time analog solver for MaxSAT, a quintessential
class of NP-hard discrete optimization problems, where the task is to find a
truth assignment for a set of Boolean variables satisfying the maximum number
of given logical constraints. We show that the scaling of an invariant of the
solver's dynamics, the escape rate, as function of the number of unsatisfied
clauses can predict the global optimum value, often well before reaching the
corresponding state. We demonstrate the performance of the solver on hard
MaxSAT competition problems. We then consider the two-color Ramsey number
$R(m,m)$ problem, translate it to SAT, and apply our algorithm to the still
unknown $R(5,5)$. We find edge colorings without monochromatic 5-cliques for
complete graphs up to 42 vertices, while on 43 vertices we find colorings with
only two monochromatic 5-cliques, the best coloring found so far, supporting
the conjecture that $R(5,5) = 43$.

20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci