Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension-Dependent behavior in the satisfability of random k-Horn
  formulae   We determine the asymptotical satisfiability probability of a random
at-most-k-Horn formula, via a probabilistic analysis of a simple version,
called PUR, of positive unit resolution. We show that for k=k(n)->oo the
problem can be ``reduced'' to the case k(n)=n, that was solved in
cs.DS/9912001. On the other hand, in the case k= a constant the behavior of PUR
is modeled by a simple queuing chain, leading to a closed-form solution when
k=2. Our analysis predicts an ``easy-hard-easy'' pattern in this latter case.
Under a rescaled parameter, the graphs of satisfaction probability
corresponding to finite values of k converge to the one for the uniform case, a
``dimension-dependent behavior'' similar to the one found experimentally by
Kirkpatrick and Selman (Science'94) for k-SAT. The phenomenon is qualitatively
explained by a threshold property for the number of iterations of PUR makes on
random satisfiable Horn formulas.

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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: physics