If G = ({S}, {a}, {S → S}, S) find the language generated by G.

If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular

O Given the language L = {(ba)m, amb", aa: m,n 2 0}, find the regular expression r such that L(r) = L.

Find a context-free grammar for each of the following languages over the alphabet {a, b}. (N: the natural number set) a. {anb2n | n ∈ N U {0}} U {an+2bn | n ∈ N} b. {ambn | m, n ∈ N, and n > m}.

Find CFGs that for these regular languages over the alphabet Σ = {a, b}. Draw a Finite Automatafirst and use this to create the CFG.(a) The language of all words that contain the substring aba.(b) The language of all words that have an odd number letters and contains the string bb.(c) The language of all words that begin with the substring ba and contains an odd number ofletters.

Show, formally in terms of DFAs, that if L0 is a regular language (has a DFA) and L1 is a regular language (has a DFA), then L0 − L1 must be a regular language as well. Show this by formalizing the difference DFA as we did in class for intersection/union.

Fast plz

Obtain a RLG and a LLG for the language L defined over the alphabet {a,b} whose wordscontain the substring ‘abba’.

2. What is the TG corresponding to the language of strings, over alphabet {a, b}, that are composed exactly of odd repetition of the substring ab, i.e. sample strings of this language are ab, ababab, ababab, etc.

Need help with part (c). Thank you :)