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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 20:32, 26 April 2012
, 20:32, 26 April 2012→6.7. Basic Notions of Formal Language Theory: markup
| <math>\underline{X} ~=~ \{ \underline{x}_1, \ldots, \underline{x}_\ell, \ldots \}.</math>
| <math>\underline{X} ~=~ \{ \underline{x}_1, \ldots, \underline{x}_\ell, \ldots \}.</math>
|}
|}
Usually, one compares different formal languages over a fixed resource, but since resources are finite it is no trouble to unite a finite number of them into a common resource. Without loss of generality, then, one typically has a fixed set <math>\underline{\underline{X}}</math> in mind throughout a given discussion and has to consider a variety of different formal languages that can be generated from the symbols of <math>\underline{\underline{X}}.</math> These sorts of considerations are aided by defining a number of formal operations on the resources <math>\underline{\underline{X}}</math> and the languages <math>\underline{X}.</math>
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The "kth power" of X, written as Xk, is defined to be the set of all sequences of length k over X.
The "kth power" of X, written as Xk, is defined to be the set of all sequences of length k over X.