Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing large and small stable models   In this paper, we focus on the problem of existence and computing of small
and large stable models. We show that for every fixed integer k, there is a
linear-time algorithm to decide the problem LSM (large stable models problem):
does a logic program P have a stable model of size at least |P|-k. In contrast,
we show that the problem SSM (small stable models problem) to decide whether a
logic program P has a stable model of size at most k is much harder. We present
two algorithms for this problem but their running time is given by polynomials
of order depending on k. We show that the problem SSM is fixed-parameter
intractable by demonstrating that it is W[2]-hard. This result implies that it
is unlikely, an algorithm exists to compute stable models of size at most k
that would run in time O(n^c), where c is a constant independent of k. We also
provide an upper bound on the fixed-parameter complexity of the problem SSM by
showing that it belongs to the class W[3].

5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
3
The categories of this paper are: physics
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex