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Recall that 3-SAT is in NP-Hard, where the 3-SAT problem is to determine whether there exists at least one way to assign
Posted: Sat May 14, 2022 8:40 pm
by answerhappygod
- Recall That 3 Sat Is In Np Hard Where The 3 Sat Problem Is To Determine Whether There Exists At Least One Way To Assign 1 (230.67 KiB) Viewed 64 times
Recall that 3-SAT is in NP-Hard, where the 3-SAT problem is to determine whether there exists at least one way to assign Boolean values to each variable in a 3-CNF formula so that the formula evaluates to True. We will define DoubleSAT as the problem of determining whether there exists at least two different ways to assign Boolean values to each variable in a 3-CNF formula so that the formula evaluates to True. Here are some examples: The formula: (x VYV2)^(XVY VZ) ^ (x VTV2)^(xVTVZ) ^ (TV Y Vz) A (TVYVZ) ^ (TVTV 2) A (TVUVZ) does not belong to DoubleSAT since there are no satisfying assignments. The formula: (XVY Vz)^(x VYVZ)^(XVTV2)^(x VTVZ)^(TVYVz)^(TVYVZ)^(TVYVz) does not belong to DoubleSAT since there is only one satisfying assignment (specifically x = True, y = True, z = True is the only satisfying assignment). The formula: (x V Y V z) 1 (x V Y V Z) ^ (x V T V z) 1 (x V T V Z) ^ (TV Y V z) ^ (TV Y V Z) does belong to DoubleSAT since there are two satisfying assignments (specifically x = True, y = True, z = True and x = True, y = True, z False both satisfy). Using a proof by reduction, demonstrate that DoubleSAT is in NP-Hard. = A - =