Discussion
What is the phase transition in random satisfiability problems?
Answer: C
Random three literal formulas are almost always satisfiable below about four point two clauses per variable and almost always unsatisfiable above it, with the hard instances concentrated at the boundary. Far from the ratio the answer is easy either way. The other options describe unrelated changes. That difficulty depends on a single structural ratio, and peaks where the answer is genuinely in doubt, is both a useful benchmarking fact and an appealing piece of science.
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