SOLUTIONS
Introduction to Automata Theory,
Languages, and Computation
Collected & Prepared By
[email protected]
13th Batch (06-07)
Dept. of Computer Science & Engineering
University of Dhaka
Copyright: No copyright
1
TABLE OF CONTENTS
SOLUTIONS FOR CHAPTER
Practice Problems for Final Exam: Solutions
CS 341: Foundations of Computer Science II
Prof. Marvin K. Nakayama
1. Short answers:
(a) Define the following terms and concepts:
i. Union, intersection, set concatenation, Kleene-star, set subtraction, complem
CS 341: Foundations of Computer Science II
Prof. Marvin Nakayama
Homework 11 Solutions
1. Answer each part TRUE or FALSE.
(a) 2n = O(n). TRUE. We can see this by letting c = 2, and noting that 2n
cn = 2n for all n 1. Thus, the definition of big-O holds f
CSE237 - Introduction to the Theory of Computation
January 24, 2002
Problem Set 1 - Solutions
Due January 31, 2002.
1. Prove by induction that for any natural number ,
divisible by 9.
is
Proof:
The proof is in two parts: the basis and the inductive ste
CS 162
Fall 2015
Homework 7 Solutions
November 19, 2015
Timothy Johnson
1. Exercise 9.2.4, pg. 391.
Let L1 , L2 , . . . , Lk be a collection of languages over alphabet such that:
For all i 6= j, Li Lj = ; i.e., no string is in two of the languages.
L1 L
CS 162
Fall 2015
Homework 6 Solutions
November 10, 2015
Timothy Johnson
1. Exercise 8.2.1(b) on page 335 of Hopcroft et al.
Show the IDs of the Turing machine of Figure 8.9 if the input tape contains 000111.
State
q0
q1
q2
q3
q4
0
(q1 , X, R)
(q1 , 0, R)
CS 341: Foundations of Computer Science II
Prof. Marvin Nakayama
Homework 9 Solutions
1. Let B be the set of all infinite sequences over cfw_0, 1. Show that B is uncountable,
using a proof by diagonalization.
Answer: Each element in B is an infinite seque
CS 341: Foundations of Computer Science II
Prof. Marvin Nakayama
Homework 13 Solutions
1. The Set Partition Problem takes as input a set S of numbers. The question is whether
the numbers can be partitioned into two sets A and A = S A such that
X
x=
xA
X
x
CS 341: Foundations of Computer Science II
Prof. Marvin Nakayama
Homework 8 Solutions
1. Consider the decision problem of testing whether a DFA and a regular expression are
equivalent. Express this problem as a language and show that it is decidable.
Answ
CS 162
Fall 2015
Homework 3 Problems
October 13, 2015
Timothy Johnson
1. Let L be the language of all string of balanced parentheses, that is, all strings of the characters
( and ) such that each ( has a matching ). Use the Pumping Lemma to show that
L is
CS 162
Fall 2015
Homework 8 Solutions
December 8, 2015
Timothy Johnson
1. Suppose an oracle has given you a magic computer, C, that when given any Boolean formula
B in CNF will tell you in one step whether B is satisfiable. Show how to use C to construct
CS 162
Fall 2015
Homework 5 Solutions
October 30, 2015
Timothy Johnson
1. Exercise 6.3.2 on page 251 of Hopcroft et al.
Convert the grammar
S 0S1 | A
A 1A0 | S |
to a PDA that accepts the same language by empty stack.
We follow the construction given in
CS 341: Foundations of Computer Science II
Prof. Marvin Nakayama
Homework 7 Solutions
1. Give an implementation-level description of a Turing machine that decides the language
B = cfw_ 0n 1n 2n | n 0 .
Answer:
M = On input string w:
1. Scan the input from
CS 162
Fall 2015
Homework 4 Problems
October 21, 2015
Timothy Johnson
1. Let L = cfw_0n 12n |n > 0 Give a CFG for L.
The following CFG will produce L.
S 0S11 | 011 |
2. Show that every regular language L is also context free. Hint: use a proof by inducti
CS 341: Foundations of Computer Science II
Prof. Marvin Nakayama
Homework 10 Solutions
1. If A m B and B is a regular language, does that imply that A is a regular language?
Answer: No. For example, define the languages A = cfw_ 0n 1n | n 0 and B = cfw_1
Learning Outcomes
Explain Groups of Layers
Explain Network Standards
Explain Why Network Standards
Explain Standard Making Process
Explain Formal Standardisation and its stages
Explain De Facto Standards
Explain International Standard Setting
Organisation
Sn 3: Learning
Outcomes
Types
of Networks: General
Future Trends
Communications media (satellite,
microwave, radio, fibre, coax)
characteristics, advantages and
disadvantages of each
Some LAN Standards: 10BaseT,
100BaseT, 1000BaseT,100BaseF,
1000BaseF
W3-1:Learning
Outcomes
Transmission
Time/Propagation time
and its implications?
What is coding (Morse Code, ASCII,
EBCDIC)
Explain Digital and Analogue definitions
Advantages of digital vs. analogue
Explain Frequency, Band, Bandwidth,
Baud rate, Bit
Hardware Fundamentals
Week 7 Lesson 1
10/09/16
Hardware Fundamentals
1
Learning Outcomes
Define Visual Display Unit (VDU) characteristics: Pixel, Resolution,
Screen size and Refresh Rate
Describe briefly the purpose of video standards.
Discuss different v
Multiplexing, Asynchronous/
Synchronous transmission
Multiplexing
Asynchronous / Synchronous transmission
Synchronous Protocols
9/10/16
1
Multiplexing
9/10/16
2
Multiplexing
Multiplexing means breaking up a higher speed
link into several slower links
W1, L1 - Learning
Outcomes
Introduction
- ice breaker.
Explain data communication theory
Explain why data communication is
important - Information Age
Identify past, present and future data
communication techniques
Demonstrate and explain a basic
com
Learning Outcomes
Explain Modulation techniques (FM, AM, PM, QAM and
TCM)
Explain modem and the different types of modems (V.32,
V.34, V.34+, V.90, V.92)
Analogue transmission of
digital signal
Problem?:
computer signal is digital,
local loop (used for
W5:L1 Learning Outcomes
Digital transmission of digital data
2 types of coding techniques,
serial/parallel transmission of an 8 bit code
digital signaling techniques :
unipolar,
bipolar (NRZ),
bipolar (RZ),
Manchester encoding
Simplex, Half duplex, F
Learning Outcomes
Compression?
Voice network circuits (PSTN, POTS)?
Local loop limitations?
PAM, PCM?
Voice Telephone Circuit
POTS (Plain Old Telephone System) or PSTN, originally
designed to carry the human voice.
voice
Frequencies that humans can hear
Wk4-1: IMPORTANT SESSION ON LAN
By the end of this session you will learn
about:
Why LANs?
Topology
components of LAN:
Repeater, Hub, Switch, Bridge, Router
Why use a LAN?
There are two main benefits to using a local area
network: information sharing and
Features
High-performance, Low-power Atmel AVR 8-bit Microcontroller
Advanced RISC Architecture
131 Powerful Instructions Most Single-clock Cycle Execution
32 8 General Purpose Working Registers
Fully Static Operation
Up to 20 MIPS Throughput at 20