# hw01 - CS 154 Intro to Automata and Complexity Theory...

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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 (five-tuple, 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 non-zero multiple...
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## This note was uploaded on 03/08/2011 for the course CS 154 taught by Professor Motwani,r during the Winter '08 term at Stanford.

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hw01 - CS 154 Intro to Automata and Complexity Theory...

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