Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Glassy Behavior and Jamming of a Random Walk Process for Sequentially
  Satisfying a Constraint Satisfaction Formula   Random $K$-satisfiability ($K$-SAT) is a model system for studying
typical-case complexity of combinatorial optimization. Recent theoretical and
simulation work revealed that the solution space of a random $K$-SAT formula
has very rich structures, including the emergence of solution communities
within single solution clusters. In this paper we investigate the influence of
the solution space landscape to a simple stochastic local search process {\tt
SEQSAT}, which satisfies a $K$-SAT formula in a sequential manner. Before
satisfying each newly added clause, {\tt SEQSAT} walk randomly by single-spin
flips in a solution cluster of the old subformula. This search process is
efficient when the constraint density $\alpha$ of the satisfied subformula is
less than certain value $\alpha_{cm}$; however it slows down considerably as
$\alpha > \alpha_{cm}$ and finally reaches a jammed state at $\alpha \approx
\alpha_{j}$. The glassy dynamical behavior of {\tt SEQSAT} for $\alpha \geq
\alpha_{cm}$ probably is due to the entropic trapping of various communities in
the solution cluster of the satisfied subformula. For random 3-SAT, the jamming
transition point $\alpha_j$ is larger than the solution space clustering
transition point $\alpha_d$, and its value can be predicted by a long-range
frustration mean-field theory. For random $K$-SAT with $K\geq 4$, however, our
simulation results indicate that $\alpha_j = \alpha_d$. The relevance of this
work for understanding the dynamic properties of glassy systems is also
discussed.

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The categories of this paper are: math
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-ph