1. (a) Let L = { x10 | x 屬於 {0,1}* } find a finite automata
M = (Q, Sigma, Delta, q0, F) such that L = L(M).
(b) Find the minimal finite automata of M.
2. A = { a^(2^n) | n >= 0 }, prove or disprove that A is a regular language.
3. Give context-free grammars over Sigma = {0,1} to generate:
(a) L1 = { w | w contains 1s more than 0s }.
n n
(b) L2 = the complement of the language L = { a b | n >= 0 }
4. Prove that every regular language is a context-free language.
5. L = { x 屬於 {a,b}* | number of a's in x > number of b's in x }, design
a pushdown automata to recognize L.
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