Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model and Objective Separation with Conditional Lower Bounds:
  Disjunction is Harder than Conjunction   Given a model of a system and an objective, the model-checking question asks
whether the model satisfies the objective. We study polynomial-time problems in
two classical models, graphs and Markov Decision Processes (MDPs), with respect
to several fundamental $\omega$-regular objectives, e.g., Rabin and Streett
objectives. For many of these problems the best-known upper bounds are
quadratic or cubic, yet no super-linear lower bounds are known. In this work
our contributions are two-fold: First, we present several improved algorithms,
and second, we present the first conditional super-linear lower bounds based on
widely believed assumptions about the complexity of CNF-SAT and combinatorial
Boolean matrix multiplication. A separation result for two models with respect
to an objective means a conditional lower bound for one model that is strictly
higher than the existing upper bound for the other model, and similarly for two
objectives with respect to a model. Our results establish the following
separation results: (1) A separation of models (graphs and MDPs) for
disjunctive queries of reachability and B\"uchi objectives. (2) Two kinds of
separations of objectives, both for graphs and MDPs, namely, (2a) the
separation of dual objectives such as reachability/safety (for disjunctive
questions) and Streett/Rabin objectives, and (2b) the separation of conjunction
and disjunction of multiple objectives of the same type such as safety,
B\"uchi, and coB\"uchi. In summary, our results establish the first model and
objective separation results for graphs and MDPs for various classical
$\omega$-regular objectives. Quite strikingly, we establish conditional lower
bounds for the disjunction of objectives that are strictly higher than the
existing upper bounds for the conjunction of the same objectives.

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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con