Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds on Syntactic Logic Expressions for Optimization Problems
  and Duality using Lagrangian Dual to characterize optimality conditions   We show that simple syntactic expressions such as existential second order
(ESO) universal Horn formulae can express NP-hard optimisation problems. There
is a significant difference between the expressibilities of decision problems
and optimisation problems. This is similar to the difference in computation
times for the two classes of problems; for example, a 2SAT Horn formula can be
satisfied in polynomial time, whereas the optimisation version in NP-hard. It
is known that all polynomially solvable decision problems can be expressed as
ESO universal ($\Pi_1$) Horn sentences in the presence of a successor relation.
We show here that, on the other hand, if $P \neq NP$, optimisation problems
defy such a characterisation, by demonstrating that even a $\Pi_0$ (quantifier
free) Horn formula is unable to guarantee polynomial time solvability. Finally,
by connecting concepts in optimisation duality with those in descriptive
complexity, we will show a method by which optimisation problems can be solved
by a single call to a "decision" Turing machine, as opposed to multiple calls
using a classical binary search setting.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: stat