NP is as easy as detecting unique solutions
Theoretical Computer Science
The design and analysis of algorithms
The design and analysis of algorithms
A linear time algorithm for unique Horn satisfiability
Information Processing Letters
On unique satisfiability and the threshold behavior of randomized reductions
Journal of Computer and System Sciences
Unique satisfiability of Horn sets can be solved in nearly linear time
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
Complexity of generalized satisfiability counting problems
Information and Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
On the Boolean connectivity problem for Horn relations
Discrete Applied Mathematics
Unique perfect phylogeny is NP-hard
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
The Complexity of Finding Multiple Solutions to Betweenness and Quartet Compatibility
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Unique perfect phylogeny is intractable
Theoretical Computer Science
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The unique satisfiability problem, that asks whether there exists a unique solution to a given propositional formula, was extensively studied in the recent years. This paper presents a dichotomy theorem for the unique satisfiability problem, partitioning the instances of the problem between the polynomial-time solvable and coNP-hard cases. We notice that the additional knowledge of a model makes this problem coNP-complete.We compare the polynomial cases of unique satisfiability to the polynomial cases of the usual satisfiability problem and show that they are incomparable. This difference between the polynomial cases is partially due to the necessity to apply parsimonious reductions among the unique satisfiability problems to preserve the number of solutions. In particular, we notice that the unique not-all-equal satisfiability problem, where we ask whether there is a unique model such that each clause has at least one true literal and one false literal, is solvable in polynomial time.