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, 13:45, 8 January 2009
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| Here also, <math>q\!</math> is a non-terminal symbol, that is, <math>q \in \{ \, ^{\backprime\backprime} S \, ^{\prime\prime} \, \} \cup \mathfrak{Q},</math> while <math>Q_1, Q_2,\!</math> and <math>W\!</math> are possibly empty strings of non-initial symbols, a fact that can be expressed in the form, <math>Q_1, Q_2, W \in (\mathfrak{Q} \cup \mathfrak{A})^*.</math> | | Here also, <math>q\!</math> is a non-terminal symbol, that is, <math>q \in \{ \, ^{\backprime\backprime} S \, ^{\prime\prime} \, \} \cup \mathfrak{Q},</math> while <math>Q_1, Q_2,\!</math> and <math>W\!</math> are possibly empty strings of non-initial symbols, a fact that can be expressed in the form, <math>Q_1, Q_2, W \in (\mathfrak{Q} \cup \mathfrak{A})^*.</math> |
| | | |
− | <pre>
| + | In practice, the couplets in <math>\mathfrak{K}</math> are used to ''derive'', to ''generate'', or to ''produce'' sentences of the corresponding language <math>\mathfrak{L} = \mathfrak{L} (\mathfrak{G}).</math> The language <math>\mathfrak{L}</math> is then said to be ''governed'', ''licensed'', or ''regulated'' by the grammar <math>\mathfrak{G},</math> a circumstance that is expressed in the form <math>\mathfrak{L} = \langle \mathfrak{G} \rangle.</math> In order to facilitate this active employment of the grammar, it is conventional to write the abstract characterization <math>(S_1, S_2)\!</math> and the specific characterization <math>(Q_1 \cdot q \cdot Q_2, \, Q_1 \cdot W \cdot Q_2)</math> in the following forms, respectively: |
− | In practice, the ordered pairs of strings in !K! are used to "derive", | |
− | to "generate", or to "produce" sentences of the language !L! = <!G!> | |
− | that is then said to be "governed" or "regulated" by the grammar !G!.
| |
− | In order to facilitate this active employment of the grammar, it is | |
− | conventional to write the characterization (S_1, S_2) in either one | |
− | of the next two forms, where the more generic form is followed by
| |
− | the more specific form:
| |
| | | |
− | | S_1 :> S_2 | + | {| align="center" cellpadding="8" width="90%" |
| | | | | |
− | | Q_1 · q · Q_2 :> Q_1 · W · Q_2
| + | <math>\begin{array}{lll} |
| + | S_1 |
| + | & :> |
| + | & S_2 |
| + | \\ |
| + | Q_1 \cdot q \cdot Q_2 |
| + | & :> |
| + | & Q_1 \cdot W \cdot Q_2 |
| + | \\ |
| + | \end{array}</math> |
| + | |} |
| | | |
| + | <pre> |
| In this usage, the characterization S_1 :> S_2 is tantamount to a grammatical | | In this usage, the characterization S_1 :> S_2 is tantamount to a grammatical |
| license to transform a string of the form Q_1 · q · Q_2 into a string of the | | license to transform a string of the form Q_1 · q · Q_2 into a string of the |