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@inproceedings{SM19,
  author={Soos, Mate and Meel, Kuldeep S.},
  title={
    BIRD: Engineering an Efficient CNF-XOR SAT Solver and its Applications to
    Approximate Model Counting
  },
  booktitle=AAAI,
  month=jan,
  year={2019},
  bib2html_rescat={Counting,Solver Engineering},
  bib2html_dl_pdf={../Papers/aaai19-sm.pdf},
  bib2html_pubtype={Refereed Conference},
  code={https://github.com/meelgroup/approxmc},
  abstract={
    Given a Boolean formula F, the problem of model counting, also referred to
    as \#SAT is to compute the number of solutions of F. Model counting is a
    fundamental problem in artificial intelligence with a wide range of
    applications including probabilistic reasoning, decision making under
    uncertainty, quantified information flow, and the like. Motivated by the
    success of SAT solvers, there has been surge of interest in the design of
    hashing-based techniques for approximate model counting for the past decade.
    We profiled the state of the art approximate model counter ApproxMC3 and
    observed that over 99.99\% of time is consumed by the underlying SAT solver,
    CryptoMinisat. This observation motivated us to ask: Can we design an
    efficient underlying CNF-XOR SAT solver that can take advantage of the
    structure of hashing-based algorithms and would this lead to an efficient
    approximate model counter?
    The primary contribution of this paper is an affirmative answer to the above
    question. We present a novel architecture, called BIRD, to handle CNF-XOR
    formulas arising from hashing-based techniques. The resulting hashing-based
    approximate model counter, called ApproxMC3, employs the BIRD framework in
    its underlying SAT solver, CryptoMinisat. To the best of our knowledge, we
    conducted the most comprehensive study of evaluation performance of counting
    algorithms involving 1896 benchmarks with computational effort totaling
    86400 computational hours. Our experimental evaluation demonstrates
    significant runtime performance improvement for ApproxMC3 over ApproMC2. In
    particular, we solve 648 benchmarks more than ApproMC2, the state of the art
    approximate model counter and for all the formulas where both ApproMC2 and
    ApproxMC3 did not timeout and took more than 1 seconds, the mean speedup is
    284.40 -- more than two orders of magnitude.
  },
}
