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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},
}