Geodesic
Calculating of logical functions probabilities in logical-probabilistic modelling of complex systems
Matematičeskoe modelirovanie, Tome 25 (2013) no. 2, pp. 125-136

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We consider possible ways to calculate probabilities of complex logical functions in logical-probabilistic modelling of poorly formalized complex systems and processes. When solving this problem basing on Zhegalkin' polynomials for given accuracy of calculations, we prove the possibility to essentially reduce the number of operations due to cutting the members with weak contagion. However, it is necessary to provide independence of logical summands in the source logical function. We show that there no such necessity if we use methods of n-tuple algebra (NTA) to calculate the probabilities. Computational complexity to calculate the probabilities precisely by our method is less than the one of the first mentioned method. Besides, both methods provide solving the inverse problem, namely the calculating of the probability for one of parameters when probabilities of the function and other parameters are given, but here it is necessary to check satisfiability for a number of delimitations.
Keywords: logical-probabilistic modelling, calculate probabilities of logical functions, Zhegalkin' polynomials, inverse problem of probabilities calculate. 
@article{MM_2013_25_2_a9,
     author = {A. E. Gorodetskii and B. A. Kulik},
     title = {Calculating of logical functions probabilities in logical-probabilistic modelling of complex systems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {125--136},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_2_a9/}
}
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A. E. Gorodetskii; B. A. Kulik. Calculating of logical functions probabilities in logical-probabilistic modelling of complex systems. Matematičeskoe modelirovanie, Tome 25 (2013) no. 2, pp. 125-136. http://geodesic.mathdoc.fr/item/MM_2013_25_2_a9/