Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of Timeline-Based Planning over Dense Temporal Domains:
  Exploring the Middle Ground   In this paper, we address complexity issues for timeline-based planning over
dense temporal domains. The planning problem is modeled by means of a set of
independent, but interacting, components, each one represented by a number of
state variables, whose behavior over time (timelines) is governed by a set of
temporal constraints (synchronization rules). While the temporal domain is
usually assumed to be discrete, here we consider the dense case. Dense
timeline-based planning has been recently shown to be undecidable in the
general case; decidability (NP-completeness) can be recovered by restricting to
purely existential synchronization rules (trigger-less rules). In this paper,
we investigate the unexplored area of intermediate cases in between these two
extremes. We first show that decidability and non-primitive recursive-hardness
can be proved by admitting synchronization rules with a trigger, but forcing
them to suitably check constraints only in the future with respect to the
trigger (future simple rules). More "tractable" results can be obtained by
additionally constraining the form of intervals in future simple rules:
EXPSPACE-completeness is guaranteed by avoiding singular intervals,
PSPACE-completeness by admitting only intervals of the forms [0,a] and
[b,$\infty$[.

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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: quant-ph