# 1. Explain the steps that a retailer might take in offering a customer a credit account. 2. What are

1. Construct a regular expression defining each of the following languages over the alphabet {a,b}: a) All strings of as and bs such that every pair of adjacent as appears before any pair of adjacent bs. (2 pts) b) All strings in which the total number of as is divisible by four, such as aabaaaabbaba. (2 pts) 2. Find finite accepter for the language L = {w: there is a symbol ai Îå not appearing in w} if the alphabetå = {a1, a2, a3}. (2 pts) 3. What is the complement of the language L accepted by the nfa onå = {a, b}: (2 pts) a l
1. Construct a regular expression defining each of the following languages over the alphabet {a,b}: a) All strings of as and bs such that every pair of adjacent as appears before any pair of adjacent bs. (2 pts) b) All strings in which the total number of as is divisible by four, such as aabaaaabbaba. (2 pts) 2. Find finite accepter for the language L = {w: there is a symbol ai Îå not appearing in w} if the alphabetå = {a1, a2, a3}. (2 pts) 3. What is the complement of the language L accepted by the nfa onå = {a, b}: (2 pts) a l l 4. a) Find a npda that accept the language L = { am bn, m£ 2 n }. (4 pts) b) Find a context-free grammar that defines the given language L. (3 pts) 5. Find CFG for the languages: a) L1 = {a x b y a zb w where x, y, z, w 0 and y x and z w and x+z=y+w } overå = {a, b}. (3 pts) b) L2 = { an bmck: çn  mç = k, n ³ 0, m³ 0, k ³ 0 } over å={a,b,c}. (3. pts) 6. Find a left linear grammar for the language L((bb+a*b*ab)*). (3 pts.) 7. Transform the grammar G with productions into Chomsky Normal Form S ® ACaS A ® BC B ® bB ½ ? C ® c ½ ? (3 pts) 8. Construct the Turing machine that will accept the language of balanced strings of parentheses on ={ ( , ) , X }. For example, the string w = (((X)XX)(XXX)) belongs to the language and will be accepted by TM, and the strings: ((X)X((XX)) and )X( are not accepted. (5 pts.) 9. Let L = { aibj ck : i¹ j or j¹ k} a) Show that the language L is a context-free language. (3 pts.) b) Show that a complementof the language L is not a context-free language. (1 pts.) 10. Construct npda that accept the following language on {a, b, c}: L = { w: a n+1 b n+m c m , n = 0, m = 0} ( 4 pts.)

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