midterm_review_v2.pdf

# 5 give an nfa for each of the following languages a

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return 0 otherwise. 5. Give an NFA for each of the following languages: (a) The language A over Σ = { 0 , 1 } of strings ends with either ”100” or ”1”. (b) The language B over Σ = { 0 , 1 } that is the complement of A . (For any language A Σ * , the complement of A is Σ * \ A ) 6. For the 2 NFA from the previous question, give an -NFA for the lan- guage B * A * , by connecting the 2 NFA using -transitions. Describe the language accepted by this automaton. 7. For the following NFA, convert it into a DFA using subset construction. 0 start 1 2 3 a b a,b b b a a 4

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5 Context-Free Languages 1. Show that all regular languages are context-free. 2. Give a CFG for each of the language below. For each CFG, find a string that is in the language and show its leftmost derivation using the CFG. (a) The language over Σ = { a, b } of words which start with an a and end with a b. (b) The language over Σ = { 0 , 1 } of palindromes whose length is even. (c) The language over Σ = { ( , ) } of matched parentheses, where each opening parenthesis is followed by a unique closing parenthesis. (d) The language over Σ = { a, b } of words that have an equal number of a ’s and b ’s. 5
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• Fall '09
• TroyVasiga
• Binary numeral system, Regular expression, MIPS assembly language program

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