k-SAT Is No Harder Than Decision-Unique-k-SAT

Authors:
Chris Calabro;Ramamohan Paturi
Affiliations:
University of California, San Diego, La Jolla, USA;University of California, San Diego, La Jolla, USA
Venue:
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Year:
2009

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Abstract

We resolve an open question by [3]: 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.