Changes

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>

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

Q_1 \cdot q \cdot Q_2

& :>

& Q_1 \cdot W \cdot Q_2

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