k-SAT Is No Harder Than Decision-Unique-k-SAT
- Cite this paper as:
- Calabro C., Paturi R. (2009) k-SAT Is No Harder Than Decision-Unique-k-SAT. In: Frid A., Morozov A., Rybalchenko A., Wagner K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg
We resolve an open question by : the exponential complexity of deciding whether a k-CNF has a solution is the same as that of deciding whether it has exactly one solution, both when it is promised and when it is not promised that the input formula has a solution. We also show that this has the same exponential complexity as deciding whether a given variable is backbone (i.e. forced to a particular value), given the promise that there is a solution. We show similar results for True Quantified Boolean Formulas in k-CNF, k-Hitting Set (and therefore Vertex Cover), k-Hypergraph Independent Set (and therefore Independent Set), Max-k-SAT, Min-k-SAT, and 0-1 Integer Programming with inequalities and k-wide constraints.
Keywordsk-SAT unique satisfiability exponential complexity quantified Boolean formulas hitting set independent set
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