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ps3-sol

# ps3-sol - ECE 468 Problem Set 3 Regular expressions Finite...

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ECE 468 Problem Set 3: Regular expressions, Finite Automata, Context-free Grammars, Parsers 1. Give the reduced DFA for the following regular expression: (( a * bcd ) | ( bc * d )) 2. For the following sub-problems, consider the following context-free grammar: S AB (1) A xAC (2) A λ (3) B CBy (4) B λ (5) C z (6) (a) What are the terminals and non-terminals of this language? Answer : V t = { x, yz } and V n = { S, A, B, C } (b) Describe the strings are generated by this language. Is this a regular language ( i.e. , could you write a regular expression that generates this language)? Answer: This language generates strings of the form x n z m + n y m . This is not regular because it requires a potentially unbounded amount of state to track how many n s and m s there are. (c) Show the derivation of the string xxzzzy starting from S (specify which produc- tion you used at each step), and give the parse tree according to that derivation. Answer: I will put a superscript on the production arrow ( ) to denote which production was used at each step.

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