Find a satisfactory assignment (if one exists) given a boolean formula in conjunctive normal form with M clauses and N literals, such that each clause contains precisely two literals. Make an implication digraph with 2N vertices (one for each literal and its negation). Include edges from y' to x and x' to y for each clause x + y. To satisfy the condition x + y, (i) if y is false, x is true, and (ii) if x is false, y is true. The formula is satisfying if and only if no variable x is in the same strong component as its negation x'. Furthermore, a topological sort of the kernel DAG (contracting each strong component to a single vertex) produces a satisfactory assignment.

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