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On the Exact Complexity of Evaluating Quantified k -CNF
2012
Algorithmica
We relate the exponential complexities 2 s(k)n of k-sat and the exponential complexity 2 s(Π 2 3-sat)n of Π23-sat (evaluating formulas of the form ∀x∃yφ(x, y) where φ is a 3-CNF in x variables and y variables) and show that s(∞) (the limit of s(k) as k → ∞) is at most s(Π23-sat). Therefore, if we assume the Strong Exponential-Time Hypothesis, then there is no algorithm for Π23-sat running in time 2 cn with c < 1. On the other hand, a nontrivial exponential-time algorithm for Π23-sat would
doi:10.1007/s00453-012-9648-0
fatcat:pqo7syfxsre4znksn3ds5ixwlu