Changes

In responding to these issues, it is advisable at first to proceed in a stepwise fashion, all the better to accommodate the chances of pursuing a series of parallel developments in the grammar, to allow for the possibility of reversing many steps in its development, indeed, to take into account the near certain necessity of having to revisit, to revise, and to reverse many decisions about how to proceed toward an optimal description or a satisfactory grammar for the language.  Doing all this means exploring the effects of various alterations and innovations as independently from each other as possible.

In responding to these issues, it is advisable at first to proceed in a stepwise fashion, all the better to accommodate the chances of pursuing a series of parallel developments in the grammar, to allow for the possibility of reversing many steps in its development, indeed, to take into account the near certain necessity of having to revisit, to revise, and to reverse many decisions about how to proceed toward an optimal description or a satisfactory grammar for the language.  Doing all this means exploring the effects of various alterations and innovations as independently from each other as possible.

The degree of intermediate organization in a grammar is measured by how many intermediate symbols it has and by how they interact with each other by means of its productions.  With respect to this issue, Grammar&nbsp;1 has no intermediate symbols at all, <math>\mathfrak{Q} = \emptyset,</math> and therefore remains at an ostensibly trivial degree of intermediate organization.  Some additions to the list of intermediate symbols are practically obligatory in order to arrive at any reasonable grammar at all, other inclusions appear to have a more optional character, though obviously useful from the standpoints of clarity and ease of comprehension.

The degree of intermediate organization in a grammar is measured by how many

intermediate symbols it has and by how they interact with each other by means

of its productions.  With respect to this issue, Grammar 1 has no intermediate

symbols at all, !Q! = {}, and therefore remains at an ostensibly trivial degree

of intermediate organization.  Some additions to the list of intermediate symbols

are practically obligatory in order to arrive at any reasonable grammar at all,

other inclusions appear to have a more optional character, though obviously

useful from the standpoints of clarity and ease of comprehension.

One of the troubles that is perceived to affect Grammar 1 is that it wastes

One of the troubles that is perceived to affect Grammar&nbsp;1 is that it wastes so much of the available potential for efficient description in recounting over and over again the simple fact that the empty string is present in the language.  This arises in part from the statement that <math>S :> S^*,\!</math> which implies that:

so much of the available potential for efficient description in recounting

over and over again the simple fact that the empty string is present in

the language.  This arises in part from the statement that S :> S*,

which implies that:

S :> S* = %e% |_| S |_| S · S |_| S · S · S |_| ...

S

& :>

& S^*

& =

& \cup & S

& \cup & S \cdot S

& \cup & S \cdot S \cdot S

|}

There is nothing wrong with the more expansive pan of the covered equation,

There is nothing wrong with the more expansive pan of the covered equation,

since it follows straightforwardly from the definition of the kleene star

since it follows straightforwardly from the definition of the kleene star