29+PS5

# 29+PS5 - Handout #29 April 25, 2011 CS103 Robert Plummer...

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Handout #29 CS103 April 25, 2011 Robert Plummer Problem Set #5—Due Monday, May 2 in class 1. Consider that following state diagram: For each of the following, give the sequence of states that the machine goes through for each of the following inputs, and indicate which are accepted: (i) abaabbba (ii) babababbbbb (iii) aaabbbaaa 2. Draw the state diagram of a DFA that accepts all strings from the following language: L = { w | w {0, 1}* and w contains neither 00 nor 11 as a substring}. [Be sure to indicate the starting state and which states are accepting.] 3. (a) Draw the state diagram for a DFA that accepts all strings over the alphabet {a, b} that contain an even number of a's or exactly two b's. (b) Characterize in English each of the states of your automaton by stating the kinds of strings that would cause the machine to end in that state. For example, one of your answers might be "State __: the machine ends here if the input string has an even number of a's." 4. Prove that all finite languages are regular.

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## This note was uploaded on 06/01/2011 for the course EE 103 taught by Professor Plummer during the Spring '11 term at Stanford.

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29+PS5 - Handout #29 April 25, 2011 CS103 Robert Plummer...

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