✎ lfa:lab03-dfa-regexp [books]

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====== DFA and RegExp Exercises ======

**Exercise 1. ** Write a Regex for IP addresses.

**Exercise 2. ** Concatenation and Kleene operators applied on languages:

**2.1.**

$math[A=\{ 0^{2k} \mid k \geq 1 \}]

$ B = \{0, \epsilon \}$
\\
$ AB = ? $
\\

**2.2.**
$math[A = \{ 0^n 1^n \mid k \geq 1 \}]
\\
$ B = \{ 1^n \mid n \geq 1 \} $
\\
$ AB = ? $ \\ $ BA = ? $

**2.3.**
$ A = \emptyset $
\\
$ B = \{ 1^n \mid n \geq 1 \} $
\\
$ AB = ? $
\\
$ A^* = ? $
\\
$ B^* = ? $
\\

**Exercise 3.** Writing Regular Expressions
\\
**3.1.** Write a regular expression for the language of arithmetic expressions containing +, * and numbers.
**Hint:** you can abbreviate $ 0 \cup 1 \cup ... \cup 9 $ by $ [0-9] $

**3.2.** Write a regular expression for $ L = \{ \omega \text{ in } \text{{0,1}} ^* \text{ | every sequence of consecutive zeros appears before ANY sequence of consecutive ones} \} $

**Exercise 4.** Write a DFA for $ L(( 10 \cup 0) ^* ( 1 \cup \epsilon )) $

**Exercise 5.** Write a regular expression which generates the accepted language of A:

{{:lfa:graf1.png?200|}}

**Exercise 6.** Simplify the regular expression you found.