# Find a CFG for univocalic words

I'm trying to figure out how to create a CFG for univocalic words...

Univocalic words are words that have only one the same vowel letter throughout the word

Example: September, Anna

Would appreciate any of your help..

• What did you try? Where did you get stuck? We're happy to help with conceptual questions but just solving homework-style exercises for you is unlikely to really help you understand. Have you noticed that the langauge here is regular? – David Richerby Sep 29 '17 at 9:33
• Here is my CFG that i created S→ CaA | CeE | CiI | CoO | CuU C→ consonant|ϵ A→ CA|aA|a|C|ϵ E→ CE|eE|e|C|ϵ I→ CI|iI|i|C|ϵ O→ CO|oO|o|C|ϵ U→ CU|oU|u|C|ϵ Example 1: S⇒CeE⇒seE⇒seCE⇒sepE⇒sepCE⇒septE⇒septeE⇒septeCE⇒septemE⇒septembeE⇒septembeC⇒september Is it correct or not? – Mona Lisa Sep 30 '17 at 1:54

Try the following grammar (which can be transformed into a regular grammar):

$S \rightarrow A \mid E \mid I \mid O\mid U$
$A \rightarrow aA \mid bA \mid cA \mid \dots \mid zA \mid \epsilon$ (all consonants and only 'a')
$E \rightarrow eE \mid bE \mid cE \mid \dots \mid zE \mid \epsilon$ (all consonants and only 'e')
$I \rightarrow iI \mid bI \mid cI \mid \dots \mid zI \mid \epsilon$ (all consonants and only 'i')
$O \rightarrow oO \mid bO \mid cO \mid \dots \mid zO \mid \epsilon$ (all consonants and only 'o')
$U \rightarrow uU \mid bU \mid cU \mid \dots \mid zU \mid \epsilon$ (all consonants and only 'u')

Example 1: $S \Rightarrow A \Rightarrow aA \Rightarrow anA \Rightarrow annA \Rightarrow annaA \Rightarrow anna$

Example 2: $S \Rightarrow E \Rightarrow sE \Rightarrow seE \Rightarrow sepE \Rightarrow septE \Rightarrow septeE \Rightarrow septemE \Rightarrow$ $septembE \Rightarrow septembeE \Rightarrow septemberE \Rightarrow september$

Warning: do not expect that this grammar generates only English dictionary words. For example it does generate a nonsense such as 'aagfdadgsa'.