Effective Algorithms for Calculation of Joint Action Spectrum in the Theory of Sufficient Causes

The paper considers efficient algorithms for calculating the spectrum of joint action of binary factors which is a tuple of joint action degrees found for sets of factors of a given response. The importance of a spectrum of joint action is that it can exhaustively describe the strength of joint action of factors in the binary theory of sufficient causes used in epidemiology, toxicology and evidence-based medicine, as well as to order the types of that joint action for a given response. The algorithms are implemented in high-level languages Java and C#. The efficiency of the algorithms is due to a new theoretical result obtained by the authors in the Boolean formalization of the binary sufficient causes theory with the help of mathematical logic, algebra and discrete mathematics, as well as due to the optimization of data storage and processing, and the use of dictionaries with hash maps without collisions. In addition, an effective algorithm is constructed to check for the presence of joint action of binary factors in a given response, based on one of these algorithms. The importance of this algorithm is due to the fact that sometimes it is necessary to quickly check the presence of joint action for a given response before determining its strength.