Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the product homomorphism problem and CQ-definability   The product homomorphism problem (PHP) takes as input a finite collection of
relational structures A1, ..., An and another relational structure B, all over
the same schema, and asks whether there is a homomorphism from the direct
product A1 x ... x An to B. This problem is clearly solvable in
non-deterministic exponential time. It follows from results in [1] that the
problem is NExpTime-complete. The proof, based on a reduction from an
exponential tiling problem, uses structures of bounded domain size but with
relations of unbounded arity. In this note, we provide a self-contained proof
of NExpTime-hardness of PHP, and we show that it holds already for directed
graphs, as well as for structures of bounded arity with a bounded domain size
(but without a bound on the number of relations). We also present an
application to the CQ-definability problem (also known as the PP-definability
problem).
  [1] Ross Willard. Testing expressibility is hard. In David Cohen, editor, CP,
volume 6308 of Lecture Notes in Computer Science, pages 9-23. Springer, 2010.

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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: math
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The categories of this paper are: hep-lat