Context Free Grammer and PDA So this a question from my book and I have to make CFG of this language but I am confused what does it mean when it says 

"L contains palindromes that don’t ever have the same character occur twice in a row."

Let Σ = {a, b, c}

Let L = {w ∈ Σ∗| w = {w1, w2, . . . , wn} is a palindrome, and wi 6= wi+1 ∀ 0 ≤ i &lt; n}.

In other words, L contains palindromes that don’t ever have the same character occur twice in a row.

In the second part can someone guide me how to make it's PDA or give an idea.
The grammar $S \to aSa \mid bSb \mid cSc \mid a \mid b \mid c \mid \epsilon$ would generate (normal) palindromes.

A simple way to extend this to generate palindromes with non-repeating would be to add for each letter $x$ a new non-terminal $S_{not\text{-}x}$, and adapt the grammar: 

$S \to aS_{not\text{-}a}a \mid \dots$ 

$S_{not\text{-}a} \to bS_{not\text{-}b}b \mid \dots$

There are probably more efficient ways.