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

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