## Problems relating Theory of Automata (Computer Theory)

Hi Everyone,

I have 4 difficult questions and I need your help on them to solve:

Q1. What would be the regular expression for the following languages (L1, L2, L3) defined over the alphabet{0,1}

L1 = The set of strings in which every 0 is followed immediately by 11.
L2 = The set of strings of 0's and 1's whose number of 0's is divisible by 5.
L3 = The set of strings of 0's and 1's whose 3rd symbol from the right is 1.

Q2. Let L be the language defined over the alphabet {a,b} such that the words in L do not contain 'bb' as a substring.
Build a deterministic Finite Automata for the language L.

Q3. Build a deterministic Finite Automata for the following Regular Expression :

(a+aab)*b

Q4. Let L2 be the language defined over the aplhabet {0,1} such that L2 consists of the set of all strings, when interpreted as a binary integer, is a multiple of 3.
For example {011, 110, 1001, ....} are the words of this language [as 011 = 3, 110 = 6, 1001 = 9]
Build a deterministic Finite Automata accepting the language L2.

Thank you in advance for help and support.