Let L be the language of all strings over alphabet Σ = {a}, such that the length of each string is either divisble by 2 or by 3, but not divisible by 6. Prove that this language is regular.

Assignment

1. Construct NFAs that recognize the specified languages

For this question use the automaton simulator shown in class, which is located at  https:automatonsimulator.com to create NFAs to recognize the following languages.

Use the save button to save the text representation of the NFAs.

(a) The language specified by where the alphabet is Σ = {x, y, z}.

(b) The language specified by (aaa|bbb|ccc)* where the alphabet is Σ ={a, b, c}.

(c) The language of all strings over Σ = {0, 1} where the sum of the digits isdivisible by4 or by 5.

2. Let L be the language of all strings over alphabet Σ = {a}, such that the length of each string is either divisble by 2 or by 3, but not divisible by 6. Prove that this language is regular.

3. Let L be the language of all strings over the alphabet Σ = {0, 1}, such that the number of 0s is less than 5 or greater than 10. Prove that this language is regular.