# A Kochen-Specker System Has at Least 22 Vectors

@article{Uijlen2016AKS, title={A Kochen-Specker System Has at Least 22 Vectors}, author={Sander Uijlen and Bas Westerbaan}, journal={New Generation Computing}, year={2016}, volume={34}, pages={3-23} }

At the heart of the Conway-Kochen Free Will Theorem and Kochen and Specker’s argument against non-contextual hidden variable theories is the existence of a Kochen-Specker (KS) system: a set of points on the sphere that has no {0,1}-coloring such that at most one of two orthogonal points are colored 1 and of three pairwise orthogonal points exactly one is colored 1. In public lectures, Conway encouraged the search for small KS systems. At the time of writing, the smallest known KS system has 31…

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## References

SHOWING 1-10 OF 24 REFERENCES

### On Searching for Small Kochen-Specker Vector Systems

- Computer Science, MathematicsWG
- 2011

A lower bound of 18 is established on the size of any KS vector system, which requires a mix of graph-theoretic and topological embedding problems, and several algorithms are proposed to tackle these problems.

### A Lower Bound on the Size of the Smallest Kochen-Specker Vector System in Three Dimensions

- Mathematics, Computer Science
- 2010

An exhaustive algorithm is given that can be used to show that the smallest KS vector system must contain at least 18 directions and how to represent KS vector systems by graphs that are not ‘101-colourable’ is shown.

### The On-Line Encyclopedia of Integer Sequences

- Computer ScienceElectron. J. Comb.
- 1994

The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.

### Kochen-Specker theorem and experimental test on hidden variables

- Physics
- 1999

A recent proposal to experimentally test quantum mechanics against noncontextual hidden-variable theories [Phys. Rev. Lett. 80, 1797 (1998)] is shown to be related with the smallest proof of the…

### A Decision Method For Elementary Algebra And Geometry

- Mathematics
- 1951

By a decision method for a class K of sentence (or other expressions) is meant a method by means of which, given any sentence θ, one can always decide in a finite number of steps whether θ is in K;…

### The Problem of Hidden Variables in Quantum Mechanics

- Physics
- 1967

Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure…

### Two simple proofs of the Kochen-Specker theorem

- Mathematics
- 1991

A new proof of the Kochen-Specker theorem uses 33 rays, instead of 117 in the original proof. If the number of dimensions is increased from 3 to 4, only 24 rays are needed.

### Quantifier elimination for real closed fields by cylindrical algebraic decomposition

- Philosophy
- 1975

Tarski in 1948, ( Tarski 1951) published a quantifier elimination method for the elementary theory of real closed fields, which provides a decision method, which enables one to decide whether any sentence of the theory is true or false.

### REDLOG: computer algebra meets computer logic

- Computer ScienceSIGS
- 1997

This work illustrates some applications of REDLOG, describes its functionality as it appears to the user, and explains the design issues and implementation techniques.

### Quantifier Elimination by Cylindrical Algebraic Decomposition — Twenty Years of Progress

- Mathematics
- 1998

The CAD (cylindrical algebraic decomposition) method and its application to QE (quantifier elimination) for ERA (elementary real algebra) was announced by the author in 1973 at Carnegie Mellon…