Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Automata Intersection Non-Emptiness: Parameterized Complexity
  Revisited   The problem DFA-Intersection-Nonemptiness asks if a given number of
deterministic automata accept a common word. In general, this problem is
PSPACE-complete. Here, we investigate this problem for the subclasses of
commutative automata and automata recognizing sparse languages. We show that in
both cases DFA-Intersection-Nonemptiness is complete for NP and for the
parameterized class $W[1]$, where the number of input automata is the
parameter, when the alphabet is fixed. Additionally, we establish the same
result for Tables Non-Empty Join, a problem that asks if the join of several
tables (possibly containing null values) in a database is non-empty. Lastly, we
show that Bounded NFA-Intersection-Nonemptiness, parameterized by the length
bound, is $\mbox{co-}W[2]$-hard with a variable input alphabet and for
nondeterministic automata recognizing finite strictly bounded languages,
yielding a variant leaving the realm of $W[1]$.

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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess