### tom's blog

By tom, history, 5 years ago,

Hello,

I'm solving problem with 2-SAT algorithm and I need to be sure that some xi will be 1 (or 0). How can I make this happen with 2SAT algorithm? When I add "xi or xi", I put xi and not xi into one SCC and 2-SAT returns me that there is no solution. Is it possible?

Thanks

• +13

 » 5 years ago, # |   +18 when you add x or x you shouldn't put them in one SCC. because you are adding 2 same sdges.
 » 5 years ago, # |   +18 If you want to force x_i to be true just add implication !x_i -> x_i.
 » 5 years ago, # |   0 It's simple: BFS over the 2-SAT graph (the skew-symmetric one) from the fixed variables while checking for contradictions. When it finishes, there will be no edge from a known variable to an unknown one. The skew-symmetricity makes sure that there's no unfixed variable from which a fixed variable can be reached afterwards, so any solution of the unfixed part of the graph + the variables you fixed this way is a solution of the original problem.