Graphs of systems of two-term equations with boolean unknowns

The paper studies Boolean systems consisting of nonlinear equations in two variables and graphs connected with them. For random system of equations an average number of solutions and a probability of absence of solution are found. For an a priori simultaneous random system of equations an average number of solutions and a distribution of the number of solutions are found. The possibility to represent such systems of equations in the form of a graph greatly simplifies the investigation.