prac_quiz1 - 6.035 Practice Quiz 1 1 Give a Regular...

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6.035 Practice Quiz 1 1. Give a Regular Expression and DFA for: L = { x ∈ { 0 , 1 } * | x ends with 1 and does not contain the substring 00 } 2. Give a RE for: L = { 0 i 1 j | i is even and j is odd } 3. Given the NFA for below for 0 * (01) * 0 * , construct a DFA: 0 0 ε ε A B D C 0 1 4. Give a RE and a DFA/NFA for the language of all strings over { 0 , 1 } * that do not end in 01. 5. Give a RE and a CFG for: L = { x ∈ { 0 , 1 } * | x starts and ends with different symbols } 6. Give a CFG for: L = { x ∈ { 0 , 1 } * | symbol at position i is same as symbol at position i+2 and | x |≥ 2 } 7. Give a CFG for the language of all non-palindromes over { 0 , 1 } * . 8. Give a CFG for: L = { 0 i 1 j 0 k | j > i + k } So, 001111100 is in the string. Hint, the concatenation of two (or more) context-free languages is context-free. 9. Eliminate left recursion from: S Aa | b A Ac | Sd | ε 10. Give a CFG for L = { a i b i c i | i 1 } . 11. Is this grammar ambiguous? If so, prove it and construct a non-ambiguous grammar that derives the same language. S aS | aSbS | c 1
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12. Assume that we have added a pointer type to decaf that can point to integers and booleans.
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