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Unformatted text preview: CS 154 Intro. to Automata and Complexity Theory Handout 3 Autumn 2008 David Dill September 29, 2009 Problem Set 1 Due: October 6, 2009 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. (20 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 of 5. Each position between the two 0’s contains an arbitrary symbol (0 or 1) from the alphabet. For example, 1001110 is not in L , but 10 111110 and 101010 1 are in L . Construct an NFA for this language.....
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 '08
 Motwani,R
 Regular expression, Automata theory

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