Formulation
The necklace problem involves the reconstruction of a necklace of n beads, each of which is either black or white, from partial information. A k-configuration in a necklace is a subset of k positions in the necklace; two configurations are isomorphic if one can be obtained from the other by a rotation of the necklace. At stage k of the reconstruction process, the partial information available at that stage is a count, for each k-configuration, of the number of k-configurations that are isomorphic to it and that contain only black beads. The necklace problem is: given n, how many stages are needed (in the worst case) in order to reconstruct the precise pattern of black and white beads in the original necklace?
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Famous quotes containing the word formulation:
“In necessary things, unity; in disputed things, liberty; in all things, charity.”
—Variously Ascribed.
The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)
“You do not mean by mystery what a Catholic does. You mean an interesting uncertainty: the uncertainty ceasing interest ceases also.... But a Catholic by mystery means an incomprehensible certainty: without certainty, without formulation there is no interest;... the clearer the formulation the greater the interest.”
—Gerard Manley Hopkins (1844–1889)
“Art is an experience, not the formulation of a problem.”
—Lindsay Anderson (b. 1923)