Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constrained Synchronization for Commutative Automata and Automata with
  Simple Idempotents   For general input automata, there exist regular constraint languages such
that asking if a given input automaton admits a synchronizing word in the
constraint language is PSPACE-complete or NP-complete. Here, we investigate
this problem for commutative automata over an arbitrary alphabet and automata
with simple idempotents over a binary alphabet as input automata. The latter
class contains, for example, the \v{C}ern\'y family of automata. We find that
for commutative input automata, the problem is always solvable in polynomial
time, for every constraint language. For input automata with simple idempotents
over a binary alphabet and with a constraint language given by a partial
automaton with up to three states, the constrained synchronization problem is
also solvable in polynomial time.

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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph