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Answer by D.W. for Counting number of assignments restricted by implications
The problem is #P-complete, hence there is no polynomial-time solution (unless P = #P). This is proved in the following paper:Hard Enumeration Problems in Geometry and Combinatorics. Nathan Linial....
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Suppose we have $n$ boolean variables, $x_1, \dots, x_n$. Some boolean variables can have implication relationships, e.g. $x_2 \implies x_5$, which means that if $x_2$ is true $x_5$ must also be true....
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