✎ lfa:2024:lab03 [books]

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====== 3. Regular Expressions ======

===== 3.1. Natural Language / DFA => Regex conversion =====

For each of the exercises from DFA Seminary 1 write a regex describing the same language.

**3.1.1.** $ L=\{w \in \{0,1\}^* \text{ | w contains an odd number of ones} \} $

{{:lfa:2022:lfa2022_lab2_ex1.png?400|}}

<hidden 3.1.1.>
$math[0^*10^*(10^*10^*)^*]
</hidden>


**3.1.2.** The language of binary words which contain **exactly** two ones

{{:lfa:2022:lfa2022_lab2_ex2.png?550|}}

<hidden 3.1.2.>
$math[0^*10^*10^*]
</hidden>

**3.1.3.** The language of binary words which encode odd numbers (the last digit is least significative)

{{:lfa:2022:lfa2022_lab2_ex3.png?300|}}

<hidden 3.1.3.>
$math[(0 \cup 1)^*1]
</hidden>


**3.1.4.** The set of all binary strings having the substring 00101

{{:lfa:2022:ex_8_dfa.png?400|}}

<hidden 3.1.4.>
$math[((1(01^*0)^*1)\cup0)^*]
</hidden>