Introduction to Java Programming and Data Structures: Brief Version (11th Global Edition)
11th Edition
ISBN: 9780134671710
Author: Y. Daniel Liang
Publisher: PEARSON
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Chapter 20, Problem 20.3PE
(Guessing the capitals) Rewrite
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1. Using one of the method described in class and/or textbook (Section 9.1) convert the following
regular expression into a state transition diagram:
(0+ 10*1)* (01 + 10)
Indicate in your answer how did you arrive at the result as follows: Write down all the state
transition diagrams that you constructed for all the subexpressions and clearly indicate which
diagram corresponds to which expression. Do not simplify any state transition diagram.
2. Consider the following state transition diagram over Σ = {a,b}:
b
A
a
a
C
b
B
a
a
b
D
За
a
Using the method described in class and in the textbook (Section 9.2) convert the diagram
into an equivalent regular expression. Include all the intermediate steps in your answer.
3. Are the languages L1, L2, and L3 below over the alphabet Σ = {a, b, c} regular or non-regular?
Justify your answer carefully.
(a) L₁ = {a¹b2jc²i : i ≥ 0, j > 2}
(b) L₂ = L₁n {akbm c³p: k,m,p≥ 0}
(c) L3 = {a²ib²j+1 : i,j ≥ 0}^{akbm c³p : k,m,p ≥ 0}
(1 point)
By dragging statements from the left column to the right column below, give a proof by induction of the following statement:
an
=
= 9" - 1 is a solution to the recurrence relation an = 9an-18 with ao
=
: 0.
The correct proof will use 8 of the statements below.
Statements to choose from:
Note that a₁ =
9a0 + 8.
Now assume that P(n) is true for all n ≥ 0.
Your Proof: Put chosen statements in order in this
column and press the Submit Answers button.
Let P(n) be the predicate, "a = 9″ – 1".
απ = 90 − 1 =
Note that
Let P(n) be the predicate, "an
9" - 1 is a
solution to the recurrence relation an = 9an-1 +8
with ao = 0."
-
Now assume that P(k + 1) is true.
Thus P(k) is true for all k.
Thus P(k+1) is true.
Then ak+1
=
9ak +8, so P(k + 1) is true.
= 1 − 1 = 0, as required.
Then = 9k — 1.
ak
Now assume that P(k) is true for an arbitrary
integer k ≥ 1.
By the recurrence relation, we have
ak+1 =
ak+1 =
= 9ak + 8 = 9(9k − 1) + 8
This simplifies to
9k+19+8 = 9k+1 − 1
Then 9k+1 − 1 = 9(9*…
Given the following request to an AI chatbot, which response is more accurate? (You should use Google to verify that the factual claims in each response are accurate.)
Prompt
Is this true? The first recorded use of the phrase "when pigs fly" in print is in a 1616 play by Ben Jonson called "The Devil is an Ass," in which a character says, "When pigs fly, good-night!!"
Response
Response A
Response B
Yes, that's true! The phrase "when pigs fly" indeed appears in Ben Jonson's 1616 play The Devil is an Ass and was said during the second act in a conversation between Fitzdottrel and Pug. The phrase was first used to express skepticism or disbelief, suggesting that something is as unlikely to happen as the fanciful idea of pigs flying. This usage is often cited as one of the earliest instances of the phrase in print.
The claim that the phrase "when pigs fly" was first recorded in Ben Jonson's 1616 play "The Devil is an Ass" is not accurate. There is no evidence from the…
Chapter 20 Solutions
Introduction to Java Programming and Data Structures: Brief Version (11th Global Edition)
Ch. 20.2 - Prob. 20.2.1CPCh. 20.2 - Prob. 20.2.2CPCh. 20.2 - Prob. 20.2.3CPCh. 20.2 - Prob. 20.2.4CPCh. 20.2 - Prob. 20.2.5CPCh. 20.3 - Prob. 20.3.1CPCh. 20.3 - Prob. 20.3.2CPCh. 20.3 - Prob. 20.3.3CPCh. 20.3 - Prob. 20.3.4CPCh. 20.4 - Prob. 20.4.1CP
Ch. 20.4 - Prob. 20.4.2CPCh. 20.5 - Prob. 20.5.1CPCh. 20.5 - Suppose list1 is a list that contains the strings...Ch. 20.5 - Prob. 20.5.3CPCh. 20.5 - Prob. 20.5.4CPCh. 20.5 - Prob. 20.5.5CPCh. 20.6 - Prob. 20.6.1CPCh. 20.6 - Prob. 20.6.2CPCh. 20.6 - Write a lambda expression to create a comparator...Ch. 20.6 - Prob. 20.6.4CPCh. 20.6 - Write a statement that sorts an array of Point2D...Ch. 20.6 - Write a statement that sorts an ArrayList of...Ch. 20.6 - Write a statement that sorts a two-dimensional...Ch. 20.6 - Write a statement that sorts a two-dimensional...Ch. 20.7 - Are all the methods in the Collections class...Ch. 20.7 - Prob. 20.7.2CPCh. 20.7 - Show the output of the following code: import...Ch. 20.7 - Prob. 20.7.4CPCh. 20.7 - Prob. 20.7.5CPCh. 20.7 - Prob. 20.7.6CPCh. 20.8 - Prob. 20.8.1CPCh. 20.8 - Prob. 20.8.2CPCh. 20.8 - Prob. 20.8.3CPCh. 20.9 - How do you create an instance of Vector? How do...Ch. 20.9 - How do you create an instance of Stack? How do you...Ch. 20.9 - Prob. 20.9.3CPCh. 20.10 - Prob. 20.10.1CPCh. 20.10 - Prob. 20.10.2CPCh. 20.10 - Prob. 20.10.3CPCh. 20.11 - Can the EvaluateExpression program evaluate the...Ch. 20.11 - Prob. 20.11.2CPCh. 20.11 - If you enter an expression "4 + 5 5 5", the...Ch. 20 - (Display words in ascending alphabetical order)...Ch. 20 - (Store numbers in a linked list) Write a program...Ch. 20 - (Guessing the capitals) Rewrite Programming...Ch. 20 - (Sort points in a plane) Write a program that...Ch. 20 - (Combine colliding bouncing balls) The example in...Ch. 20 - (Game: lottery) Revise Programming Exercise 3.15...Ch. 20 - Prob. 20.9PECh. 20 - Prob. 20.10PECh. 20 - (Match grouping symbols) A Java program contains...Ch. 20 - Prob. 20.12PECh. 20 - Prob. 20.14PECh. 20 - Prob. 20.16PECh. 20 - (Directory size) Listing 18.10,...Ch. 20 - Prob. 20.20PECh. 20 - (Nonrecursive Tower of Hanoi) Implement the...Ch. 20 - Evaluate expression Modify Listing 20.12,...
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