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Unformatted text preview: CS 154 Intro. to Automata and Complexity Theory Handout 3 Autumn 2006 David Dill October 3, 2006 Problem Set 1 Due: October 10, 2006 Homework: (Total 100 points) Do the following exercises. For a question that requires the specification of a finite automaton, in the absence of further instructions, your solution may use any one of the no tations in the textbook (fivetuple, transition diagram, or transition table). Problem 1. (10 points) Provide DFAs for the following languages over the alphabet Σ = { , 1 } . (a). All strings that contain at least two instances of the substring 01. (b). All strings that do not end with 111. Problem 2. (15 points) Let M be a DFA such that for some state q ∈ Q and for all a ∈ Σ, δ ( q, a ) = q . Use induction on strings to show that for all w ∈ Σ * , b δ ( q, w ) = q. Problem 3. (25 points) (a). [5 points] Let L ⊂ { , 1 } * be the language of all strings such that there are two 0’s separated by a number of positions that is a nonzero multiple...
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 Winter '08
 Motwani,R
 Following, Automata theory, DFA Records, Transition function

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