Question 5. Consider the language L over the alphabet (a, b } such that L = {a²b³n>0, m> 0 }. a) Develop a PDA for the language L without developing the CFG. (CFG to PDA conversion should not be used)/ b) Develop a CFG for L

Give a CFG that generates the language defined by the regular expression ((ab* a) | (b(aa)*b))+ over the alphabet {a,b}. Show how you would modify your CFG for the regular expression ((ab*a) | (b(aaa)*b))+.

(1) When is a language L called as regular? (2) Prove that language L = {wa" b:m 2 0, w € {a, b}*} is regular by design a dfa or an nfa to accept it. (3) If you designed an nfa in (2), convert it to a dfa.

2) Give a DFA (both state transition diagram and table as well as description of each state) for each of the following languages a) A language over alphabet E = {0,1,2,3,4,5,6,7} in which reverse of each string (for instance, reverse of 1234 is 4321) interpreted as an octadecimal (base-8) number is a multiple of 3. (for example: 14, 47, 135, 512, 702, 4001, 41713, e.t.c) (Hint: Consider inductive contruction wnew gerse, where a denotes any symbol from E and then try to figure out the states of DFA with respect to possible values of a and the length of wold-) reverse Wold. a which means wnew a. W.