Homework set #7 solutions, Math 128A
J. Xia
Sec 4.4: 1a, 2a, 3a, 7abc, 17 1a. Compute by hand or use a program. Matlab code for the Composite Trapezoidal rule: function integral = cmptrap(a,b,n,f) h = (b-a)/n; x = [a+h:h:b-h]; integral = h/2*(2*sum(feval(

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Assignment #10-alt: Matrix Factorization and Matrix Norms Due date: Wednesday, November 24, 2010 (10:10am) For full credit you must show all of your work.
# 4 "12 8 & % ( 1. Consider the matrix A = %"12 40 "28( . % 8 "28 29 ( $ '
a. Derive the factorizati

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CS 172, Spring 1999 Midterm #1 Professor Manuel Blum
This is a CLOSED BOOK examination. Calculators ARE permitted. Do all your work on the pages of this examination. Problem #1 a) Define the number of steps taken by

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0,1
Prelim 1 March 3, 1997
B
0 0 0,1 1 1
A
D
C
0,1
b. Write a regular expression that accepts the same lan

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1 April 9, 1993
1. (20 points) Recall that any language, L, falls into one of four categories: (a) L is recursive (b) L is r.e. but not recursive (c) L is r.e. but not recursive (d) Neither L nor L are r.e. Note that

Name CS-172 David Wolfe 1. De ne
x
1 Quiz 2 March 12, 1993
Each of the following questions counts equally. Try to keep your answers succinct.
p
to be the parity bit of 2 f0 1g .
x p
x
=
0 if has an even number of 1's 1 if has an odd number of 1

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1 February 12, 1993
Each of the following questions counts equally. Try to keep your answers succinct.
Pumping Lemma: If is regular then
(9n)(8z 2
L L
jzj
n)(9uvw
such that =
z L.
uvw
and juvj
n
and jvj 1)(8i)

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S.A. Seshia
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YOUR NAME:
Instructions: This exam is closed-book, open-notes. Please turn off electronic devices: cell phones, laptops, PDAs, etc. You have a total of 70 minutes. The

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YOUR NAME :
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This exam is open-book, open-notes. Please turn off electronic devices: cell phones, laptops, PDAs, etc.
You have a total of 180

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Problem 1: [True or False, with justification] (30 points)
For each of the following questions, state TRUE or FALSE. Justify your answer in brief, indicating only the proof idea or counterexample, drawing an annotated

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S. A. Seshia and A. Kulkarni
Midterm 1
February 26, 2008
YOUR NAME :
Instructions:
This exam is closed-book, open-notes. Please turn off and put away electronic devices such
as cell phones, laptops, etc.
Y

CS 172: Computability and Complexity, Spring 2010
S. A. Seshia and O. Etesami
Midterm 1
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YOUR NAME :
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Professor Luca Trevisan
Solutions to Midterm 1
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Solutions to Midterm 1
1. Every day, a weather station records whether the day was sunny (S ), cloudy (C ) or rainy
(R). A sequence of reco

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Professor Luca Trevisan
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Solutions to Midterm 2
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T

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S. A. Seshia & O. Etesami
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CS 172 | Fall 2000 Computability and Complexity
A = fw 2 f0 1g : w = wR g. B = fw 2 f0 1g : w 6= wR g. Here, wR is the word w reversed. Prove your answers.
Prelim 2 November 8, 2000
Problem 1. (50 points) Determine which of the following two langua

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Problem 1. (100 points) Given a word w, the stutter reduction w] is the word that results from
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CS172, Midterm 2, Spring 1999
CS 172, Spring 1999 Midterm Exam 2 Manual Blum
q q q q q
q
This is a CLOSED BOOK examination. Calculators ARE permitted. Do all your work on the pages of this examination. For most problems, you may answer YES, NO, "

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Acknowledgments: L.von Ahn, L. Blum, M. Blum, R. Jhala
A Card Game: SET
A 'Set' is 3 cards in which for every feature: either it is the SAME o