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The "FS2/Theory" page has been changed by brane: http://wiki.apache.org/subversion/FS2/Theory?action=diff&rev1=3&rev2=4 * πΉ is the set of all data configurations; * πΉ: πΉ Γ πΉ βΆ β is a metric on πΉ. - '''Definition:''' A ''configuration history'' is a sequence of elements of the data configuration space. + '''Definition:''' A ''configuration history'' is a sequence of elements of the data configuration space; in other words, it is a ''curve'' in (πΉ, πΉ). == Defining the Metric == @@ -23, +23 @@ π: πΉ Γ πΉ βΆ β^0^ applied to the binary-digit sequence representation of data configurations. It is easy to showβ that π has all the required properties of a metric. In addition, it has the following properties: - * The minimum distance between any two distinct configurations isβ 1. + * The minimum distance between any two distinct configurations is 1. - * The maximum distance between any two distinct configurations isβ the greater of their sizes: βa,b β πΉ: π(a, b) β€ max(''S'',,a,,, ''S'',,b,,) . + * The maximum distance between any two distinct configurations is the greater of their sizes: βa,b β πΉ: π(a, b) β€ max(''S'',,a,,, ''S'',,b,,), - * And it follows from this that: βc β πΉ: π(π, c) = ''S'',,c,, . + * from wich it follows that: βc β πΉ: π(π, c) = ''S'',,c,,. + == The History Curve == +
