Abstract
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.
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Cadoli, M., Schaerf, M. (2006). Partial Solutions with Unique Completion. In: Stock, O., Schaerf, M. (eds) Reasoning, Action and Interaction in AI Theories and Systems. Lecture Notes in Computer Science(), vol 4155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11829263_6
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DOI: https://doi.org/10.1007/11829263_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37901-0
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