Chapter 3 - Exercises
(100%)
1.
(24%; 4% each) U se REs to express the following languages .
(a) All strings with as or bs appearing in pairs (at least one pair).
(b) All strings of symbols over alphabet cfw_ a , b, each containing alternating as and bs.
I
6-7-2011
Linear Algebra ()
100 (Linearization)
()
(i)
(ii) active and alive SIAM
(SIMAX)
(iii)
1G. Strang, Linear Algebra and Its Applications, 4th edition, Brooks/ Cole,
2006.
2. K. Hoffman and R. Kunze, Linear Algebra, 2nd edition, Prentice-Hall,
Tsung-Yi Ho
tyho@cs.nctu.edu.tw
http:/eda.nctu.edu.tw/tyho
Department of Computer Science
National Chiao Tung University
Hsinchu, Taiwan
1
Ch 7
Outline
1
2
Pushdown Automata and Context-Free Languages
3
2
Nondeterministic Pushdown Automata
Deterministic
Tsung-Yi Ho
tyho@cs.nctu.edu.tw
http:/eda.nctu.edu.tw/tyho
Department of Computer Science
National Chiao Tung University
Hsinchu, Taiwan
1
Ch 6
Outline
1
2
Two Important Normal Form
3
2
Methods for Transforming Grammars
A Membership Algorithm for CFGs*
C
Computer Networks: An Open Source Approach
Chapter 8
Solutions to Chapter 8
Hands-on: (25 points each)
2. Setup iptables to block the outgoing connection to a certain IP address, and try to
see whether the blocking work.
Answer:
You can add a new rule to
Chapter 3
Arithmetic for Computers
Tien-Fu Chen
Material source:
COD4 slides
Dept. of Computer Science
National Chiao Tung Univ.
Numbers: Possible Representations
Bits are just bits (no inherent meaning)
data meaning depends on interpretation of bits
Sig
Sept. 28, 2012
2
3
4
5
Minimum of 6 characters
6
7
Should the content be
memorized? This may be
the case when dealing with
equipment limitation and
emergency procedures?
8
9
Input the maximum number of
courses the User can manage
at a time. It does not li
Arithmetic Coding
Arithmetic Coding
Huffman coding has been proven the best
fixed length coding method available.
Yet, since Huffman codes have to be an
integral number of bits long, while the
entropy value of a symbol may (as a matter
of fact, almost alw
The Adaptive Loop Filtering Techniques in the HEVC Standard
Ching-Yeh Chena, Chia-Yang Tsaia, Yu-Wen Huanga, Tomoo Yamakageb, In Suk Chongc,
Chih-Ming Fua, Takayuki Itohb, Takashi Watanabeb, Takeshi Chujohb, Marta Karczewiczc, and
Shaw-Min Leia
a
MediaTek
S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani
181
6.4 Knapsack
During a robbery, a burglar nds much more loot than he had expected and has to decide what
to take. His bag (or knapsack) will hold a total weight of at most W pounds. There are n
items t
Chapter 10 - Exercises
(100%)
1. (10%) L ist all the truth assignments, which satisfy the Boolean expression E = x zy) xz).
(
(
Use 0 for false and 1 for true.
2. (20%) Problem H1 m ay be reduced to problem H 2 i n time complexity of O ( n 2 ) where n i s
I
7-11-2011
Ch2 Linear Transformations and Matrices
, ,
.
F.
2.1 Linear Transformations, Null spaces, and ranges
H.W. 1, 9, 12, 14, 21, 23
Definition: Let V and W be vector spaces. We call a function T : V W a linear
transformation (or linear) from
I
Ch4 Determinants
(The determinant) special scalar-valued function M nn ( F ) .
numerical linear algebra ,.
. eigenvalues
eigenvalues .
4.1 2 2 . 4.2, 4.2 & 4.3
n n . 4.5 ,
M nn ( F ) F .(i) n-linear (ii) alternating (iii) ( I ) 1 .
( det A ).
(i)
I
Ch3 Elementary Matrix Operations and Systems of Linear
Equations
,
.:
Ax b.
A M nn ( F ) x R n , b R n , x ,b .A .
Ax b . rank (
3.2). elementary matrix operations and elementary matrices(3.1).
3.1 Elementary Matrix Operations and Elementary Matrice
Linear Algebra
Chapter 3
Determinants and Eigenvectors
3.1 Introduction to Determinants
Definition
The determinant () of a 2 2 matrix A is denoted |A| and
is given by
a11 a12
= a11a22 a12 a21
a21 a22
Observe that the determinant of a 2 2 matrix is given
Linear Algebra
Chapter 7
Inner Product Spaces
Inner Product Spaces
In this chapter, we extend those concepts of Rn such as:
dot product of two vectors, norm of a vector, angle between
vectors, and distance between points, to general vector space.
This w
Linear Algebra
Chapter 8
Numerical Technique
8.1 Gaussian Elimination
Definition
A matrix is in echelon form if
1. Any rows consisting entirely of zeros are grouped at the
bottom of the matrix.
2. The first nonzero element of each row is 1. This element
Linear Algebra
Chapter 2
Matrices and Linear
Transformations
2.1 Addition, Scalar Multiplication,
and Multiplication of Matrices
aij: the element of matrix A in row i and column j.
Definition
Two matrices are equal if they are of the same size and if t
Linear Algebra
Chapter 6
Linear Transformations
6.1 Introduction to Linear Transformations
Definition
Let U and V be vector spaces. A transformation T: U V is a
mapping that assigns to each vector u in U a unique vector v in
V.
Definition
Let U and V be
Linear Algebra
Chapter 4
General Vector Spaces
4.1 General Vector Spaces and Subspaces
Our aim in this section will be to focus on the algebraic properties
of Rn. We draw up a set of axioms () based on the properties
of Rn. Any set that satisfies these
Linear Algebra
Chapter 1
Linear Equations and Vectors
1.1 Matrices and Systems of
Linear Equations
Definition
An equation () in the variables () x and y that
can be written in the form ax+by=c, where a, b, and c are
real constants () (a and b not both
Linear Algebra
Chapter 5
Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors
Definition
Let A be an n n matrix. A scalar is called an eigenvalue (
,) of A if there exists a nonzero vector x in Rn such that
Ax = x.
The vector x is called an eig