Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Optimal Decision Procedure for MPNL over the Integers   Interval temporal logics provide a natural framework for qualitative and
quantitative temporal reason- ing over interval structures, where the truth of
formulae is defined over intervals rather than points. In this paper, we study
the complexity of the satisfiability problem for Metric Propositional Neigh-
borhood Logic (MPNL). MPNL features two modalities to access intervals "to the
left" and "to the right" of the current one, respectively, plus an infinite set
of length constraints. MPNL, interpreted over the naturals, has been recently
shown to be decidable by a doubly exponential procedure. We improve such a
result by proving that MPNL is actually EXPSPACE-complete (even when length
constraints are encoded in binary), when interpreted over finite structures,
the naturals, and the in- tegers, by developing an EXPSPACE decision procedure
for MPNL over the integers, which can be easily tailored to finite linear
orders and the naturals (EXPSPACE-hardness was already known).

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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
37
The categories of this paper are: supr-con
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga