Editing Regular grammar (section)

== Examples ==
An example of a right-regular grammar ''G'' with ''N'' = {S, A}, Σ = {a, b, c}, ''P'' consists of the following rules
: S → aS
: S → bA
: A → ε
: A → cA
and S is the start symbol. This grammar describes the same language as the [[regular expression]] a*bc*, viz. the set of all strings consisting of arbitrarily many "''a''"s, followed by a single "''b''", followed by arbitrarily many "''c''"s.

A somewhat longer but more explicit extended right-regular grammar ''G'' for the same regular expression is given by ''N'' = {S, A, B, C}, Σ = {a, b, c}, where ''P'' consists of the following rules:
: S → A
: A → aA
: A → B
: B → bC
: C → ε
: C → cC
...where each uppercase letter corresponds to phrases starting at the next position in the regular expression.

As an example from the area of programming languages, the set of all strings denoting a floating point number can be described by an extended right-regular grammar ''G'' with ''N'' = {S,A,B,C,D,E,F}, Σ = {0,1,2,3,4,5,6,7,8,9,+,−,.,e}, where S is the start symbol, and ''P'' consists of the following rules:

:{| 
|-
|| S → +A &nbsp; &nbsp; &nbsp; || A → 0A &nbsp; &nbsp; &nbsp; || B → 0C &nbsp; &nbsp; &nbsp; || C → 0C &nbsp; &nbsp; &nbsp; || D → +E &nbsp; &nbsp; &nbsp; || E → 0F &nbsp; &nbsp; &nbsp; || F → 0F
|-
|| S → −A || A → 1A || B → 1C || C → 1C || D → −E || E → 1F || F → 1F
|-
|| S →  A || A → 2A || B → 2C || C → 2C || D →  E || E → 2F || F → 2F
|-
||             || A → 3A || B → 3C || C → 3C ||             || E → 3F || F → 3F
|-
||             || A → 4A || B → 4C || C → 4C ||             || E → 4F || F → 4F
|-
||             || A → 5A || B → 5C || C → 5C ||             || E → 5F || F → 5F
|-
||             || A → 6A || B → 6C || C → 6C ||             || E → 6F || F → 6F
|-
||             || A → 7A || B → 7C || C → 7C ||             || E → 7F || F → 7F
|-
||             || A → 8A || B → 8C || C → 8C ||             || E → 8F || F → 8F
|-
||             || A → 9A || B → 9C || C → 9C ||             || E → 9F || F → 9F
|-
||             || A → .B ||             || C → eD ||             ||             || F → ε
|-
||             || A →  B ||             || C → ε ||      ||             ||
|}