hw03 - CS 154 Intro to Automata and Complexity Theory...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 154 Intro. to Automata and Complexity Theory Handout 10 Autumn 2006 David Dill October 17, 2006 Problem Set 3 Due: October 24, 2006 Homework: (Total 100 points) Do the following exercises. Problem 1. [15 points] (Exercise 4.2.6(c) on page 147 of the second edition of the textbook) Show that the regular languages are closed under the following operation: init ( L ) = { w | for some x, wx is in L } . Hint : It is easiest to start with a DFA for L and perform a construction to get the desired language. Problem 2. [40 points] Give an algorithm to solve the following deci- sion problems. In each case you can assume that you are given a concrete representation of the language in the form of DFA. You must justify the correctness of the algorithm to receive full credit. a). Suppose L is a regular language over the alphabet Σ = { 0 , 1 } . Give an algorithm to decide whether | L | ≥ 100. b). Suppose L is a regular language over the alphabet Σ = { 0 , 1 } . Give an algorithm to decide whether L contains any string w such that w has zero occurrences of the patterns 00 and 11. Problem 3. [10 points] Prove that { 0 n 1 m 2 n - m | n m 0 } is not a regular language. Problem 4. [10 points]
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern