Construct an nfa that accepts the language L((a|b)* ab(a|b))

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

Let L, and L2 be the languages defined as follows: L1 ={ xe{0,1}* | x has an odd number of Os}. L2 ={ 0"1m0" | n, m 20} Which of the following context-free grammars generates the language L1 U L2? (Here all uppercase letters are variables) O E- 1E| OF F- 1F| OE je A- OAO | B B - 1B|E OS-E|A E - OF | 1E F- OE | 1F|E A- OAO | 1A|E OS- S1 | S2 S1 → 00S | 15 | 01A| 10A | B A- 10S | 01S B-1|8 S2→ OS,0| A2 A2 - 1| S2|E S-E|A E- 1E| OF F- 1F| OE je A- OAO | B B- 1B|E

a) Construct a push-down automaton that accepts the language L = {a't°c*[i = j or i=k for i> 0}.