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Unformatted text preview: CSE 105: Introduction to the Theory of Comptuation Fall 2010 Problem Set 2 Instructor: Daniele Micciancio Due on: Wed. Oct 13, 2010 Guidelines: Same as for homework 1. Solutions to the homework should be submitted electronically using turnin, and you should submit a single pdf le together with 4 j ap les (2a.j ,2b.j ,3a.j ,3b.j ), all zipped according to the instructions on the class website. Problem 1 (6 points) Transform the following regular expressions into equivalent NFAs using the procedure studied in class (also described in the textbook). You can simplify your answer to some extent (e.g., by omitting some redundant-transitions), but your NFAs should have a structure that closely correspond to the given regular expressions. 1. ((0 * 1 * ) * 01) + 10(0 + 1) * An NFA which recognizes this language: 1. 1(11) * + (00) * A pair of NFAs which recognize this language: 1. 2. Problem 2 (8 points) Consider the Very Simple Automata (VSA) as de ned in homework 1. (Please refer to the de nition of VSA in the posted solutions, rather than your own solutions to hw1.) In this problem you are asked to prove that VSA are not more powerful than regular DFA, i.e., any problem that can be solved using a VSA can also be solved using a DFA. This is intuitively obvious, as VSAs seem simpler than DFA, but we want to rigorously prove that this intuition is correct. Speci cally, as part of your solution, you should give the mathematical description of a transformation that turns any DFA M = ( Q, Σ ,δ,s,F ) into a VSA V = ( Q , Σ ,δ ,s ,F ) that recognizes the same language L ( M ) = L ( V ) . Your solution should also include a brief explanation of the main ideas behind your solution, and a justi cation of your claim that the two automata accept the same language. Optionally, you can also give a formal proof that the DFAlanguage....
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- Spring '10
- Formal language, Regular expression, Regular language, Nondeterministic finite state machine, Automata theory