Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constrained Counting and Sampling: Bridging the Gap between Theory and
  Practice   Constrained counting and sampling are two fundamental problems in Computer
Science with numerous applications, including network reliability, privacy,
probabilistic reasoning, and constrained-random verification. In constrained
counting, the task is to compute the total weight, subject to a given weighting
function, of the set of solutions of the given constraints. In constrained
sampling, the task is to sample randomly, subject to a given weighting
function, from the set of solutions to a set of given constraints.
Consequently, constrained counting and sampling have been subject to intense
theoretical and empirical investigations over the years. Prior work, however,
offered either heuristic techniques with poor guarantees of accuracy or
approaches with proven guarantees but poor performance in practice.
  In this thesis, we introduce a novel hashing-based algorithmic framework for
constrained sampling and counting that combines the classical algorithmic
technique of universal hashing with the dramatic progress made in combinatorial
reasoning tools, in particular, SAT and SMT, over the past two decades. The
resulting frameworks for counting (ApproxMC2) and sampling (UniGen) can handle
formulas with up to million variables representing a significant boost up from
the prior state of the art tools' capability to handle few hundreds of
variables. If the initial set of constraints is expressed as Disjunctive Normal
Form (DNF), ApproxMC is the only known Fully Polynomial Randomized
Approximation Scheme (FPRAS) that does not involve Monte Carlo steps. By
exploiting the connection between definability of formulas and variance of the
distribution of solutions in a cell defined by 3-universal hash functions, we
introduced an algorithmic technique, MIS, that reduced the size of XOR
constraints employed in the underlying universal hash functions by as much as
two orders of magnitude.

36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int