Geodesic
The number of solutions of some types of systems of Boolean equations
Diskretnaya Matematika, Tome 1 (1989) no. 1, pp. 105-116.

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We consider two different types of systems of Boolean equations—those given in disjunctive normal form and those in the form of a sum $\operatorname{mod}2$ of elementary conjunctions. We obtain exact formulas for the average number of solutions and the asymptotics of the typical number of solutions. For this purpose we identify the explicit distinction among the various types of systems in the sense of the effect of the parameters of the system on the number of solutions. 
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T. M. Igamberdiev. The number of solutions of some types of systems of Boolean equations. Diskretnaya Matematika, Tome 1 (1989) no. 1, pp. 105-116. http://geodesic.mathdoc.fr/item/DM_1989_1_1_a9/