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@inproceedings{PMM21,
  title={
    On the Usefulness of Linear Modular Arithmetic in Constraint Programming
  },
  author={Pesant, Gilles and Meel, Kuldeep S. and Mohammadalitajrishi, Mahshid},
  booktitle=CPAIOR,
  bib2html_pubtype={Refereed Conference},
  year={2021},
  month=jul,
  bib2html_rescat={Counting},
  bib2html_dl_pdf={../Papers/cpaior21-pmm.pdf},
  abstract={
    Linear modular constraints are a powerful class of constraints that arise
    naturally in cryptanalysis, checksums, hash functions, and the like. Given
    their importance, the past few years have witnessed the design of
    combinatorial solvers with native support for linear modular constraints,
    and the availability of such solvers has led to the emergence of new
    applications. While there exist global constraints inCPthat consider
    congruence classes over domain values,linear modular arithmetic constraints
    have yet to appear in the global constraint catalogue despite their past
    investigation in the context of model counting for CSPs. In this work we
    seek to remedy the situation by advocating the integrationof linear modular
    constraints in state-of-the-ar tCP solvers.Contrary to previous belief, we
    conclude from an empirical investigation that Gauss-Jordan Elimination based
    techniques can provide an efficient and scalable way to handle linear
    modular constraints. On the theoretical side, we remark onthe pairwise
    independence offered by hash functions based on linear modular constraints,
    and then discuss the design of hashing-based model counters for CP,supported
    by empirical results showing the accuracy and computational savings that can
    be achieved. We further demonstrate the usefulness of native support for
    linear modular constraints with applications to checksums and model counting
  },
}