Question

1. Construct a DFSM to accept the language: L w E ab): w contains at least 3 as and no more than 3 bs) 2. Let E (acgt and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg. ge. Construct both a DFSM to accept the language and a regular expression that represents the language. 3. Let ab. For a string w E , let w denote the string w with the a's and b's flipped. For example, for w = aabbab: w bbaaba wRbabbaa-abaabb Construct a PDA to accept the language: L [ww 4. Let E (ab.cd). Construct a PDA to accept the language = L (a"b cd:m +n = p + q} 5. Write down a context-free grammar for the language: {a'b':2i 3j+ 1 6. Here is the context-free grammar for the language of arithmetic expressions presented in class: EE+T E T T T F TF F(E) Fid Write down a derivation of the string (id + id) * id + id. Draw the parse tree that results from that derivation 7. Show that the above language of arithmetic expressions is not regular.

Answer 1

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A for given cala Ca a a VJ VB V0 b /5 オa at ta, c9, 9 CA t oalaro palba 98 ae/aa biblbb Scanned with CamScanner

LSw cwl We latb)と J IE w Conlains abb then apter c tene ghauld be bba azo/azo ala Vo a,9le 3 Robzblb aale arble Bibibb b,aba a b/ab acceptane w abbc bba ofecance wabcb CS Scanned with CamScanner

(5) alb arat) S ABb A aaAle 1g9 9 g aag bbb muftbe QCapled ABb S aa AB b Qaag bbbBb aaag bbbb (6) R P T PJ ) Scanned with CamScanner

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