The Complexity of Unique -SAT: An Isolation Lemma for -CNFs
نویسندگان
چکیده
We provide some evidence that Unique -SAT is as hard to solve as general -SAT, where -SAT denotes the satisfiability problem for -CNFs and Unique SAT is the promise version where the given formula has or solutions. Namely, defining for each , a -time randomized algorithm for -SAT and, similarly, a -time randomized algorithm for Unique -SAT , we show that . As a corollary, we prove that, if Unique -SAT can be solved in time for every , then so can -SAT for all . Our main technical result is an isolation lemma for CNFs, which shows that a given satisfiable -CNF can be efficiently probabilistically reduced to a uniquely satisfiable -CNF, with non-trivial, albeit exponentially small, success probability.
منابع مشابه
The Complexity of Unique k-SAT: An Isolation Lemma for k-CNFs
We provide some evidence that Unique k-SAT is as hard to solve as general k-SAT, where k-SAT denotes the satisfiability problem for k-CNFs with at most k literals in each clause and Unique k-SAT is the promise version where the given formula has 0 or 1 solutions. Namely, defining for each k > 1, sk = inf{δ > 0 | ∃ a O(2)-time randomized algorithm for k-SAT} and, similarly, σk = inf{δ > 0 | ∃ a ...
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