Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a more efficient approach for the satisfiability of two-variable
  logic   We revisit the satisfiability problem for two-variable logic, denoted by
SAT(FO2), which is known to be NEXP-complete. The upper bound is usually
derived from its well known Exponential Size Model (ESM) property. Whether it
can be determinized efficiently is still an open question.
  In this paper we present a different approach by reducing it to a novel
graph-theoretic problem that we call Conditional Independent Set (CIS). We show
that CIS is NP-complete and present two simple algorithms for it with run time
O(1.4423^n) and O(1.6181^n), where n is the number of vertices in the graph. We
also show that unless the "Strong Exponential Time Hypothesis" (SETH) fails,
there is no algorithm for CIS with run time O(1.4141^n).
  We show that without the equality predicate SAT(FO2) is in fact equivalent to
CIS in succinct representation. This yields two algorithms for SAT(FO2) without
the equality predicate with run time O(1.4423^{2^n}) and O(1.6181^{2^n}), where
n is the number of predicates. To the best of our knowledge, these are the
first exact algorithms for an NEXP-complete decidable logic with run time
significantly lower than O(2^{2^n}). We also identify a few lower complexity
fragments of FO2 which correspond to the tractable fragments of CIS. Similar to
CIS, unless SETH fails, there is no algorithm for SAT(FO2) with run time
O(1.4141^{2^n}).
  For the fragment with the equality predicate, we present a linear time
many-one reduction to the fragment without the equality predicate. The
reduction yields equi-satisfiable formulas with a small constant blow-up in the
number of predicates. Finally, we also perform some small experiments which
show that our approach is indeed more promising than the existing method (based
on the ESM property). The experiments also show that although theoretically it
has the worse run time, the second algorithm in general performs better than
the first one.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc