Let $L$ be a regular language with alphabet $\Sigma = \{a,b,c\}$.

Prove that the following language is regular:

$\{w | w \in L \text{ and } w \text{ starts with } abc \}$.

I wonder what proof strategy I can use to prove this.

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Use closure properties of regular languages.

  • $\begingroup$ $\{w | w \in L \text{ and } w \text{ starts with } abc \} = L \cap abc(a|b|c)^*$. And regular languages are closed under intersection. Am I right? $\endgroup$ – fornit Jun 5 '17 at 21:21
  • $\begingroup$ Right, that's the simplest proof. $\endgroup$ – Yuval Filmus Jun 5 '17 at 21:40

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