Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Journal of Symbolic Computation
Isomorph-free exhaustive generation
Journal of Algorithms
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
On searching for small kochen-specker vector systems
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
On searching for small kochen-specker vector systems
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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Kochen-Specker (KS) vector systems are sets of vectors in ℝ3 with the property that it is impossible to assign 0s and 1s to the vectors in such a way that no two orthogonal vectors are assigned 0 and no three mutually orthogonal vectors are assigned 1. The existence of such sets forms the basis of the Kochen-Specker and Free Will theorems. Currently, the smallest known KS vector system contains 31 vectors. In this paper, we establish a lower bound of 18 on the size of any KS vector system. This requires us to consider a mix of graph-theoretic and topological embedding problems, which we investigate both from theoretical and practical angles. We propose several algorithms to tackle these problems and report on extensive experiments. At the time of writing, a large gap remains between the best lower and upper bounds for the minimum size of KS vector systems.