Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
8th Edition
ISBN: 9781259676512
Author: Kenneth H Rosen
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 13.2, Problem 5E
Find the output for each of these input strings when given as input to the finite-state machine in Example 2.
a) 0111 b) 11011011 c) 01010101010
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Exercise 5.11.2: Counting binary strings.
Count the number of binary strings of length 10 subject to each of the following restrictions.
There is only one binary string of length ten with no 1's: 00000000000. There are 210 binary strings of length ten. Therefore the number of binary strings of length ten with at least one 1 is 210 - 1.
(b)
The string has at least one 1 and at least one 0.
(c)
The string contains exactly five 1's or it begins with a 0.
Exercise 5.11.4: Counting integer multiples.
(b)
How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?
Let S be the set of all bit strings (strings of 0's and I's)
Select one:
O A. f(s) = the string obtained by moving the first bit of s to the end of the string. (For example, f(1001101) = 0011011)
O B. f(s) = the string obtained from s by interchanging 0's and I's. (For example, f(11000) = 00111)
O c. f(s) the string & with a 1 bit appended at the end. (For example, f(1101) = 11011)
O D. f(s) the reversal of s. (For example, f(110) = 011)
length at least 2. Which of the following functions f : S → S is not onto S?
The number 0.60 is rational and can be represented in finitely many digits in decimal
a. can it be represented by finetly many bits in binary? explain why or why not.
b. if it can be done in finitely many bits, give its exact binary representation. if not, give the first ten bits of the approxijmate representation.
c. give an upper bound on absolute error in this representation.
Chapter 13 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Ch. 13.1 - Exercises 1-3 refer to the grammar with start...Ch. 13.1 - Exercises 1-3 refer to the grammar with start...Ch. 13.1 - Prob. 3ECh. 13.1 - Let G=(V,T,S,P) be the phrase-structure grammar...Ch. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Show that the grammar given in Example 5 generates...Ch. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
Ch. 13.1 - Construct a derivation of 021222 in the grammar...Ch. 13.1 - Show that the grammar given in Example 7 generates...Ch. 13.1 - s13. Find a phrase-structure grammar for each of...Ch. 13.1 - Find a phrase-structure grammar for each of these...Ch. 13.1 - Find a phrase-structure grammar for each of these...Ch. 13.1 - Construct phrase-structure grammars to generate...Ch. 13.1 - Construct phrase-structure grammars to generate...Ch. 13.1 - Construct phrase-structure grammars to generate...Ch. 13.1 - Prob. 19ECh. 13.1 - A palindrome is a string that reads the same...Ch. 13.1 - Let G1 and G2 be context-free grammars, generating...Ch. 13.1 - Prob. 22ECh. 13.1 - Construct derivation trees for the sentences in...Ch. 13.1 - Let G be the grammar with V={a,b,c,S};T={a,b,c} ;...Ch. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - a) Explain what the productions are in a grammar...Ch. 13.1 - Prob. 29ECh. 13.1 - a) Construct a phrasestructure grammar for the set...Ch. 13.1 - Give production rules in Backus-Naur form for an...Ch. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Prob. 36ECh. 13.1 - Prob. 37ECh. 13.1 - Prob. 38ECh. 13.1 - Prob. 39ECh. 13.1 - Prob. 40ECh. 13.1 - Prob. 41ECh. 13.1 - Let G be a grammar and let R be the relation...Ch. 13.2 - Draw the state diagrams for the finite-state...Ch. 13.2 - Give the state tables for the finite-state machine...Ch. 13.2 - Find the output generated from the input string...Ch. 13.2 - Find the output generated from the input string...Ch. 13.2 - Find the output for each of these input strings...Ch. 13.2 - Find the output for each of these input strings...Ch. 13.2 - Construct a finite-state machine that models an...Ch. 13.2 - Prob. 8ECh. 13.2 - Construct a finite-state machine that delays an...Ch. 13.2 - Construct a finite-state machine that changes...Ch. 13.2 - Construct a finite-state machine for the log-on...Ch. 13.2 - Construct a finite-state machine for lock that...Ch. 13.2 - Construct a finite-state machine for a toll...Ch. 13.2 - Construct a finite-state machine for entering a...Ch. 13.2 - Construct a finite-state machine for a restricted...Ch. 13.2 - Construct a finite-state machine that gives an...Ch. 13.2 - Prob. 17ECh. 13.2 - Construct a finite-state machine that determines...Ch. 13.2 - Construct a finite-state machine that determines...Ch. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Find the output string generated by the Moore...Ch. 13.2 - Prob. 23ECh. 13.2 - Construct a Moore machine that gives an output of...Ch. 13.2 - Prob. 25ECh. 13.3 - Prob. 1ECh. 13.3 - 2. Show that if A is a set of strings, then.
Ch. 13.3 - Find all pairs of sets of strings A and B for...Ch. 13.3 - Show that these equalities hold. a) {}*={} b)...Ch. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Determine whether the string 01001 is in each of...Ch. 13.3 - Determine whether each of these strings is...Ch. 13.3 - Determine whether each of these strings is...Ch. 13.3 - Determine whether all the strings in each of these...Ch. 13.3 - Show that if M=(S,I,f,so,F) is a deterministic...Ch. 13.3 - Given a finite-state automaton M=(S,I,f,so,F) ,...Ch. 13.3 - In Exercises 16—22 find the language recognized by...Ch. 13.3 - In Exercises 16—22 find the language recognized by...Ch. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - In Exercises 16—22 find the language recognized by...Ch. 13.3 - In Exercises 16—22 find the language recognized by...Ch. 13.3 - Prob. 22ECh. 13.3 - Construct a deterministic finite-state automaton...Ch. 13.3 - Construct a deterministic finite-state automaton...Ch. 13.3 - Construct a deterministic finite-state automaton...Ch. 13.3 - Construct a deterministic finite-state automaton...Ch. 13.3 - Prob. 27ECh. 13.3 - Construct a deterministic finite-state automaton...Ch. 13.3 - Prob. 29ECh. 13.3 - Construct a deterministic finite-state automaton...Ch. 13.3 - Construct a deterministic finite-state automaton...Ch. 13.3 - Construct a deterministic finite-state automaton...Ch. 13.3 - Prob. 33ECh. 13.3 - Prob. 34ECh. 13.3 - Prob. 35ECh. 13.3 - Prob. 36ECh. 13.3 - Prob. 37ECh. 13.3 - Prob. 38ECh. 13.3 - Prob. 39ECh. 13.3 - Use Exercise 39 finite-state automata constructed...Ch. 13.3 - Prob. 41ECh. 13.3 - Prob. 42ECh. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - In Exercises 43-49 find the language recognized by...Ch. 13.3 - Prob. 47ECh. 13.3 - In Exercises 43-49 find the language recognized by...Ch. 13.3 - Prob. 49ECh. 13.3 - Find a deterministic finite-state automaton that...Ch. 13.3 - Prob. 51ECh. 13.3 - Find a deterministic finite-state automaton that...Ch. 13.3 - Find a deterministic finite-state automaton that...Ch. 13.3 - Find a deterministic finite-state automaton that...Ch. 13.3 - Find a deterministic finite-state automaton that...Ch. 13.3 - Find a nondeterministic finite-state automaton...Ch. 13.3 - Prob. 57ECh. 13.3 - Prob. 58ECh. 13.3 - Prob. 59ECh. 13.3 - Prob. 60ECh. 13.3 - Prob. 61ECh. 13.3 - Prob. 62ECh. 13.4 - Describe in words the strings in each of these...Ch. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Express each of these sets using a regular...Ch. 13.4 - Express each of these sets using a regular...Ch. 13.4 - Express each of these sets using a regular...Ch. 13.4 - Construct deterministic finite-state automata that...Ch. 13.4 - Construct nondeterministic finite-state automata...Ch. 13.4 - Construct nondeterministic finite-state automata...Ch. 13.4 - Show that if A is a regular set, then AR, the set...Ch. 13.4 - Using the construction described in the proof of...Ch. 13.4 - Using the construction described in the proof of...Ch. 13.4 - Construct a nondeterministic finite-state...Ch. 13.4 - In Exercises 15-17 conflict a regular grammar...Ch. 13.4 - In Exercises 15-17 conflict a regular grammar...Ch. 13.4 - In Exercises 15-17 conflict a regular grammar...Ch. 13.4 - Show that the finite-state automaton constructed...Ch. 13.4 - Show that the regular grammar constructed from a...Ch. 13.4 - Show that every nondeterministic finite-state...Ch. 13.4 - Let M=(S,I,f,s0,F) be a deterministic finite-state...Ch. 13.4 - One important technique used to prove that certain...Ch. 13.4 - Show that the set 02n1nn=0,1,2,... is not regular...Ch. 13.4 - Show that the set {1n2n=0,1,2,...} is not regular...Ch. 13.4 - Show that the set of palindromes over {0, 1} is...Ch. 13.4 - Prob. 26ECh. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Prob. 29ECh. 13.4 - Prob. 30ECh. 13.4 - Use Exercise 29 to show that the language...Ch. 13.5 - Let T be the Turing machine defined by the...Ch. 13.5 - Let T be the Turing machine defined by the...Ch. 13.5 - What does the Turing machine defined by the...Ch. 13.5 - What does the Turing machine described by the...Ch. 13.5 - What does the Turing machine described by the...Ch. 13.5 - Construct a Turing machine with tape 0, 1, and B...Ch. 13.5 - Construct a Turning machine with tape symbols 0,...Ch. 13.5 - Construct a Turing machine with tape symbols 0, 1,...Ch. 13.5 - Construct a Turing machine with tape symbols 0, 1,...Ch. 13.5 - Construct a Turing machine with tape symbols 0, 1,...Ch. 13.5 - Construct a Turing machine that recognizes the set...Ch. 13.5 - Construct a Turing machine that recognizes the set...Ch. 13.5 - Construct a Turing machine that recognizes the set...Ch. 13.5 - Show at each step the contents of the tape of the...Ch. 13.5 - Explain why the Turing machine in Example 3...Ch. 13.5 - Construct a Turing machine that recognizes the set...Ch. 13.5 - Construct a Turing machine that recognizes the set...Ch. 13.5 - Construct a Turing machine that computes the...Ch. 13.5 - Construct a Turing machine that computes the...Ch. 13.5 - Construct a Turing machine that computes the...Ch. 13.5 - Construct a Turing machine that computes the...Ch. 13.5 - Construct a Turing machine that computes the...Ch. 13.5 - Construct a Turing machine that computes the...Ch. 13.5 - Construct a Turing machine that computes the...Ch. 13.5 - Construct a Turing machine that computes the...Ch. 13.5 - Construct a Turning machine that computes the...Ch. 13.5 - Prob. 27ECh. 13.5 - Prob. 28ECh. 13.5 - Which of the following problems is a decision...Ch. 13.5 - Which of the following problems is a decision...Ch. 13.5 - Prob. 31ECh. 13.5 - Show that the function B(n) cannot be computed by...Ch. 13 - a) Define a phrase-structure grammar. b) What does...Ch. 13 - a) What is the language generated by a...Ch. 13 - Prob. 3RQCh. 13 - Prob. 4RQCh. 13 - Prob. 5RQCh. 13 - a) What is a finite-state machine? b) Show how a...Ch. 13 - Prob. 7RQCh. 13 - Prob. 8RQCh. 13 - Prob. 9RQCh. 13 - Prob. 10RQCh. 13 - a) Define a nondeterministic finite-state...Ch. 13 - a) Define the set of regular expressions over a...Ch. 13 - Prob. 13RQCh. 13 - Prob. 14RQCh. 13 - Prob. 15RQCh. 13 - Prob. 16RQCh. 13 - Describe how Turing machines are used to recognize...Ch. 13 - Prob. 18RQCh. 13 - Prob. 19RQCh. 13 - Prob. 1SECh. 13 - Prob. 2SECh. 13 - Prob. 3SECh. 13 - Prob. 4SECh. 13 - Prob. 5SECh. 13 - Prob. 6SECh. 13 - Prob. 7SECh. 13 - Prob. 8SECh. 13 - Prob. 9SECh. 13 - Prob. 10SECh. 13 - Prob. 11SECh. 13 - Prob. 12SECh. 13 - Prob. 13SECh. 13 - Construct a finite-state machine with output that...Ch. 13 - Construct a finite-state machine with output that...Ch. 13 - Prob. 16SECh. 13 - Prob. 17SECh. 13 - Prob. 18SECh. 13 - Construct a deterministic finite-state automaton...Ch. 13 - Prob. 20SECh. 13 - Prob. 21SECh. 13 - Prob. 22SECh. 13 - Prob. 23SECh. 13 - Prob. 24SECh. 13 - Prob. 25SECh. 13 - Show that {02nnN} is not regular. You may use the...Ch. 13 - Prob. 27SECh. 13 - Prob. 28SECh. 13 - Construct a Turing machine that computes the...Ch. 13 - Prob. 30SECh. 13 - Prob. 1CPCh. 13 - Prob. 2CPCh. 13 - Prob. 3CPCh. 13 - Prob. 4CPCh. 13 - Given the state table of a Moore machine and an...Ch. 13 - Given the state table of a Mealy machine and an...Ch. 13 - Given the state table of a deterministic...Ch. 13 - Prob. 8CPCh. 13 - Prob. 9CPCh. 13 - Prob. 10CPCh. 13 - Given a regular grammar, construct a finite-state...Ch. 13 - Given a finite-state automaton, construct a...Ch. 13 - Prob. 13CPCh. 13 - Solve the busy beaver problem for two states by...Ch. 13 - Prob. 2CAECh. 13 - Prob. 3CAECh. 13 - Prob. 4CAECh. 13 - Prob. 5CAECh. 13 - Prob. 1WPCh. 13 - Describe the Backus-Naur form (and extended...Ch. 13 - Explain how finite-state machines are used by...Ch. 13 - Explain how finite-state machines are used in the...Ch. 13 - Explain how finite-state machines are used in...Ch. 13 - Compare the use of Moore machines versus Mealy...Ch. 13 - Explain the concept of minimizing finite-state...Ch. 13 - Give the definition of cellular automata, Explain...Ch. 13 - Define a pushdown automaton. Explain how pushdown...Ch. 13 - Define a linear-bounded automaton. Explain how...Ch. 13 - Prob. 11WPCh. 13 - Prob. 12WPCh. 13 - Prob. 13WPCh. 13 - Show that a Turing machine can simulate any action...Ch. 13 - Prob. 15WPCh. 13 - Describe the basic concepts of the lambda-calculus...Ch. 13 - Show that a Turing machine as defined in this...Ch. 13 - Prob. 18WP
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