On total functions, existence theorems and computational complexity
Theoretical Computer Science
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
The relative complexity of NP search problems
Journal of Computer and System Sciences
The OPL optimization programming language
The OPL optimization programming language
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation
Journal of Automated Reasoning
CSPLIB: A Benchmark Library for Constraints
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Compiling problem specifications into SAT
Artificial Intelligence - Special volume on reformulation
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In this paper we investigate the computational complexity of combinatorial problems with givens, i.e., partial solutions, and where a unique solution is required. Examples for this article are taken from the games of Sudoku, N-queens and related games. We will show the computational complexity of many decision and search problems related to Sudoku, a number of similar games and their generalization. Furthermore, we propose a logical description of several such problems that can lead to a formulation in the language of Quantified Boolean Formulae (QBF) and, hence, their mechanization via a QBF solver. Some experiments on finding the minimum number of givens necessary/sufficient to guarantee uniqueness of solution are shown.