Programmable Logic Controllers
5th Edition
ISBN: 9780073373843
Author: Frank D. Petruzella
Publisher: McGraw-Hill Education
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Chapter 2, Problem 12RQ
What are the advantage and the disadvantage of using high-density modules?
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Big-Omega.
Consider this code:
def f(n) \\n is natural number >=1
x = n
while x 1:
if x % 2 == 0:
else:
x = x/2
x = 2*x - 2
Determine the best possible lower bound for the number of iterations of the while
loop. Use this bound to determine the complexity class of the function f.
Proof of correctness of iterative algorithms
The algorithm Occur (A, f,l,x) below returns the number of occurrences of or in
array A between positions f and 1. More precisely, it satisfies the following precon-
dition/postcondition pair:
Precondition: A is an array, f and I are integers such that 1 ≤ ƒ ≤ i ≤
length(A).
Postcondition: The integer returned by the algorithm is the number of elements
of the following set: {j: f≤ j ≤l^A[j] = x}.
Occur (A, f, 1, x)
t = 0
i = f
while i<=1 {
if A[i] == x {
t = t +1
}
}
i = i + 1
return t
Provide a complete proof of correctness of this algorithm.
Average case complexity
Consider this function:
def put (1st, first, last, value):
i = last
while i
last = i
first and value < 1st [i]:
last = last
i-i-1
-
1
1st [last] value
return 1st
Assume 1st is a list of integers, value is an integer, and first <= last are nat-
ural numbers. For the purpose of our computations, we will define n-last-first+1
(the size of 1st). Also, assume the elements of 1st are almost sorted, in the sense
that the probability that each element of the array has a probability of being out of
order with a distance m units from its correct place m, 0 ≤m ≤ n − 1, is propor-
tional with, that is this probability equals 1. In order to determine c, keep in
mind that all involved probabilities sum to 1. Additionally, you may use the formula
Inn (which is true for large n) to determine the value of c. Once you
have determined the value of c, compute the average runtime of the function put
and determine its complexity class.
m+1
Chapter 2 Solutions
Programmable Logic Controllers
Ch. 2 - Prob. 1RQCh. 2 - What is the function of a PLC output interface...Ch. 2 - Prob. 3RQCh. 2 - Prob. 4RQCh. 2 - Prob. 5RQCh. 2 - Prob. 6RQCh. 2 - Prob. 7RQCh. 2 - Prob. 8RQCh. 2 - Prob. 9RQCh. 2 - Prob. 10RQ
Ch. 2 - Prob. 11RQCh. 2 - What are the advantage and the disadvantage of...Ch. 2 - With reference to PLC discrete input modules: a....Ch. 2 - Prob. 14RQCh. 2 - Explain the function of the backplane of a PLC...Ch. 2 - Prob. 16RQCh. 2 - Prob. 17RQCh. 2 - Prob. 18RQCh. 2 - What electronic element can be used as the...Ch. 2 - With reference to discrete output module current...Ch. 2 - What electronic element can be used as the...Ch. 2 - Prob. 22RQCh. 2 - Prob. 23RQCh. 2 - Prob. 24RQCh. 2 - Prob. 25RQCh. 2 - Prob. 26RQCh. 2 - Prob. 27RQCh. 2 - Prob. 28RQCh. 2 - Prob. 29RQCh. 2 - Explain the difference between a unipolar and...Ch. 2 - Prob. 31RQCh. 2 - In what two ways can the loop power for current...Ch. 2 - Prob. 33RQCh. 2 - Prob. 34RQCh. 2 - Prob. 35RQCh. 2 - Write a short explanation for each of the...Ch. 2 - Write a short explanation for each of the...Ch. 2 - Prob. 38RQCh. 2 - Prob. 39RQCh. 2 - Prob. 40RQCh. 2 - Prob. 41RQCh. 2 - Prob. 42RQCh. 2 - Prob. 43RQCh. 2 - Prob. 44RQCh. 2 - Prob. 45RQCh. 2 - Prob. 46RQCh. 2 - Prob. 47RQCh. 2 - What information is normally stored in the ROM...Ch. 2 - Prob. 49RQCh. 2 - Prob. 50RQCh. 2 - Prob. 51RQCh. 2 - Prob. 52RQCh. 2 - Prob. 53RQCh. 2 - Prob. 54RQCh. 2 - Prob. 55RQCh. 2 - Prob. 56RQCh. 2 - Prob. 57RQCh. 2 - Prob. 58RQCh. 2 - Prob. 59RQCh. 2 - Prob. 60RQCh. 2 - What is the function of a transducer?Ch. 2 - Prob. 62RQCh. 2 - Prob. 1PCh. 2 - Assume a thermocouple, which supplies the input to...Ch. 2 - With reference to I/O module specifications: a. If...Ch. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - Prob. 6P
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