QCA models involve a number of conditions and outcomes whose subset and superset relations are analyzed and framed in terms of necessity and sufficiency. If some condition or combination of conditions is a superset of the outcome, the former is necessary for the latter. If some condition or combination of conditions is a subset of the outcome, the former is sufficient for the latter.
Three related variants of QCA exist: crisp-set QCA (csQCA), multi-value QCA (mvQCA) and fuzzy-set QCA (fsQCA). A subvariant of csQCA called temporal QCA (tQCA) is suitable for event sequence relations. The QCA package provides extensive functionality for all of these variants.
The ``exact'' Quine-McCluskey algorithm for crisp sets has been implemented for csQCA and mvQCA since version 0.6-0, and fsQCA as well as tQCA since version 1.0-0. Starting with version 0.4-5 the package has a new function called "eqmcc" (enhanced Quine-McCluskey) which finds exact solutions much faster and with substantially lower memory consumption (Dusa 2007, 2010). Since version 1.0-4, some intensive computationally parts of the R code were compiled in the C language, considerably increasing the speed even further.
How to make the most of R's and the QCA package's capabilities is demonstrated in detail with many examples by Thiem and Dusa (2012).
A. Dusa. A Mathematical Approach to the Boolean Minimization Problem. Quality & Quantity, 44(1):99-113, 2010.
C. C. Ragin. The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. University of California Press, Berkeley, 1987.
C. C. Ragin. Fuzzy-Set Social Science, University of Chicago Press, Chicago, 2000.
C. C. Ragin. Redesigning Social Inquiry: Fuzzy Sets and Beyond. University of Chicago Press, Chicago, 2008.
A. Thiem and A. Dusa. Qualitative Comparative Analysis with R: A User's Guide. Springer, New York, 2012.