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Why are instances far from the critical ratio easy?

  • A.Such instances contain fewer variables than critical ones
  • B.The solver's heuristics are tuned for those regions
  • C.The formulas can be simplified to propositional form
  • D.Solutions are abundant below it and contradictions obvious above it

Answer: D

With few clauses almost any assignment works and local search finds one immediately, while with very many the contradiction is shallow and propagation reveals it quickly. Only near the boundary is the answer genuinely uncertain and the search long. Variable counts, tuning and simplification are not the reason. That difficulty is greatest where the answer is least predictable is intuitive once stated and it generalises well beyond satisfiability. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

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