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Designing Samplers is Easy: The Boon of Testers

Designing Samplers is Easy: The Boon of Testers.
Priyanka Golia, Mate Soos, Sourav Chakraborty and Kuldeep S. Meel.
In Proceedings of Formal Methods in Computer-Aided Design (FMCAD), October 2021.

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Abstract

Given a formula F, the problem of uniform sampling seeks to sample solutions of F uniformly at random. Uniform sampling is a fundamental problem with a wide variety of applications. The computational intractability of uniform sampling has led to the development of several samplers that are heuristics and are not accompanied by theoretical analysis of their distribution. Recently, Chakraborty and Meel (2019) designed the first scalable sampling tester, Barbarik, based on a grey-box sampling technique for testing if the distribution, according to which the given sampler is sampling, is close to the uniform or far from uniform. While the theoretical analysis of Barbarik provides only unconditional soundness guarantees, the empirical evaluation of Barbarik did show its success in determining that some of the off-the-shelf samplers were far from a uniform sampler. The availability of Barbarik has the potential to spur the development of samplers and testing techniques such that developers can design sampling methods that can be accepted by Barbarik even though these samplers may not be amenable to a detailed mathematical analysis. In this paper, we present the realization of this aforementioned promise. Based on the flexibility offered by CryptoMiniSat, we design a sampler CMSGen that promises the achievement of the sweet spot of the quality of distributions and runtime performance. In particular, CMSGen achieves significant runtime performance improvement over the existing samplers. We conduct two case studies, and demonstrate that the usage of CMSGen leads to significant runtime improvements in the context of combinatorial testing and functional synthesis. A salient strength of our work is the simplicity of CMSGen, which stands in contrast to complicated algorithmic schemes developed in the past that fail to attain the desired quality of distributions with practical runtime performance.

BibTeX

@inproceedings{GSCM21,
  title={Designing Samplers is Easy: The Boon of Testers},
  author={
    Golia, Priyanka and Soos, Mate and Chakraborty, Sourav and Meel, Kuldeep S.
  },
  booktitle=FMCAD,
  year={2021},
  month=oct,
  bib2html_rescat={Sampling,Distribution Testing},
  bib2html_dl_pdf={../Papers/fmcad21.pdf},
  bib2html_pubtype={Refereed Conference},
  abstract={
    Given a formula F, the problem of uniform sampling seeks to sample solutions
    of F uniformly at random. Uniform sampling is a fundamental problem with a
    wide variety of applications. The computational intractability of uniform
    sampling has led to the development of several samplers that are heuristics
    and are not accompanied by theoretical analysis of their distribution.
    Recently, Chakraborty and Meel (2019) designed the first scalable sampling
    tester, Barbarik, based on a grey-box sampling technique for testing if the
    distribution, according to which the given sampler is sampling, is close to
    the uniform or far from uniform. While the theoretical analysis of Barbarik
    provides only unconditional soundness guarantees, the empirical evaluation
    of Barbarik did show its success in determining that some of the
    off-the-shelf samplers were far from a uniform sampler.
    The availability of Barbarik has the potential to spur the development of
    samplers and testing techniques such that developers can design sampling
    methods that can be accepted by Barbarik even though these samplers may not
    be amenable to a detailed mathematical analysis. In this paper, we present
    the realization of this aforementioned promise. Based on the flexibility
    offered by CryptoMiniSat, we design a sampler CMSGen that promises the
    achievement of the sweet spot of the quality of distributions and runtime
    performance. In particular, CMSGen achieves significant runtime performance
    improvement over the existing samplers. We conduct two case studies, and
    demonstrate that the usage of CMSGen leads to significant runtime
    improvements in the context of combinatorial testing and functional
    synthesis.
    A salient strength of our work is the simplicity of CMSGen, which stands in
    contrast to complicated algorithmic schemes developed in the past that fail
    to attain the desired quality of distributions with practical runtime
    performance.
  },
}

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