Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Intersection Problem for Finite Monoids   We investigate the intersection problem for finite monoids, which asks for a
given set of regular languages, represented by recognizing morphisms to finite
monoids from a variety V, whether there exists a word contained in their
intersection. Our main result is that the problem is PSPACE-complete if V is
contained in DS and NP-complete if V is non-trivial and contained in DO. Our
NP-algorithm for the case that V is contained in DO uses novel methods, based
on compression techniques and combinatorial properties of DO. We also show that
the problem is log-space reducible to the intersection problem for
deterministic finite automata (DFA) and that a variant of the problem is
log-space reducible to the membership problem for transformation monoids. In
light of these reductions, our hardness results can be seen as a generalization
of both a classical result by Kozen and a theorem by Beaudry, McKenzie and
Therien.

24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn