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hw1sol

# hw1sol - CSE105 Homework Number 1 SOLUTIONS October 6 2010...

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Unformatted text preview: CSE105 Homework Number 1 SOLUTIONS October 6, 2010 Guidelines: solutions to the homework should be submitted electronically, following the instructions on the class website. As part of your solutions to this assignment you should submit: 1. A le with the text of your solutions to all 4 problems, in pdf format. 2. 4 j ap les containing the automata for problems 2 and 3. The main le should be in pdf format (no doc les, etc.) and be clearly divided into 4 sections (and respective subsections) corresponding to the 4 problems. There is no j ap le for problems 1 and 4. All your les (writeup.pdf,2a.j ,2b.j ,3a.j ,3b.j ) should be named and zipped together according to the instructions. Homeworks should be submitted on the due date before class time. 1 Simple DFA questions Let M be the DFA with states Q = { q 1 ,q 2 ,q 3 ,q 4 ,q 5 }, input alphabet Σ = { u,d } , transition function δ , start state q 2 and accept states F = { q 2 } where δ is given by the following transition table. δ q 1 q 2 q 3 q 4 q 5 u q 5 q 1 q 2 q 3 q 4 d q 2 q 3 q 4 q 5 q 1 1. Give 3 example strings that are accepted by the DFA Starting from state q 2 , each of the following strings causes the DFA to go (possibly through a series of states) to state q 2 (the only accepting state) (a) The empty string is accepted because the DFA starts in state q 2 which is an accept state. (b) dduu The string ddud takes the DFA from state q 2 to q 3 to q 4 to q 3 to q 2 . (c) uuuuduu The string uuuuu takes the DFA from state q 2 to q 1 to q 5 to q 4 to q 3 to q 4 to q 3 to q 2 . 2. Give 3 example strings that are not accepted by the DFA (a) u The string u is not accepted because it takes the machine from q 2 to q 1 , which is not an accept state. (b) uuuuuu The string ud is accepted because it takes the DFA from state q 2 to q 1 to q 5 to q 4 to q 3 to q 2 to q 1 . 1 (c) ddud The string ddud takes the DFA from state q 2 to q 3 to q 4 to q 3 to q 4 , which is not an accept state. 3. Give a high level English description of M using complete sentences and proper grammar and punctu- ation. This description should be no more than two reasonably short sentences Where C u is de ned as the number of occurences of u and C d is de ned as the number of occurences of d in a string s, s will be accepted by this DFA if and only if C u modulo 5 is equal to C d modulo 5....
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hw1sol - CSE105 Homework Number 1 SOLUTIONS October 6 2010...

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