...items

For CSPs, these items are all possible variable-value pairs.

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...items

The lattice of sets can also represent problems where each variable can have a different number of assigned values.

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...states

The ket notation is conceptually similar to the use of boldface to denote vectors and distinguish them from scalars.

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...becomes

66#66 is the transpose of U with all elements changed to their complex conjugates. That is 67#67.

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...obtained

I thank J. Gilbert for pointing out this technique, as a variant of the orthogonal Procrustes problem [24].

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...numerically

High precision values were obtained from the FindRoot function of Mathematica.

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...algorithm

The values are given in Online Appendix 1.

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...degree

Using the Mathematica function Rationalize and the package NumberTheory`Recognize`.

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...nogood

I thank J. Lamping for suggesting this.

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...evaluation

I thank S. Vavasis for suggesting this improvement in the classical simulation of the algorithm.

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...problems

That is, problems generated by random selection of nogoods without regard for whether they have a solution.

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...point

This differs slightly from the results for problems with more specified structure on the nogoods, such as explicitly removing the necessary nogoods from consideration [50, 53].

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...solubility

This is a particularly large error for this theory: it does better for problems with larger constraints or more allowed values per variable.

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...nogoods

This differs slightly from other studies of random 3SAT in not allowing duplicate clauses in the propositional formula.

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...solution

For the values of 245#245 and small problems examined here, there are enough soluble instances randomly generated that there is no need to rely on a prespecified solution to efficiently find soluble test problems.

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