Discrete Mathematics With Applications
5th Edition
ISBN: 9780357035283
Author: EPP
Publisher: Cengage
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Chapter 12.2, Problem 29ES
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Design a finite-state automaton to accept the language defined by the regular expression in the referenced exercise from Section
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Chapter 12 Solutions
Discrete Mathematics With Applications
Ch. 12.1 - If x and y are strings, the concatenation of x and...Ch. 12.1 - Prob. 2TYCh. 12.1 - Prob. 3TYCh. 12.1 - Prob. 4TYCh. 12.1 - Prob. 5TYCh. 12.1 - Prob. 6TYCh. 12.1 - Prob. 7TYCh. 12.1 - Use of a single dot in a regular expression stands...Ch. 12.1 - Prob. 9TYCh. 12.1 - If r is a regular expression, the notation r +...
Ch. 12.1 - Prob. 11TYCh. 12.1 - Prob. 12TYCh. 12.1 - Prob. 1ESCh. 12.1 - Prob. 2ESCh. 12.1 - Prob. 3ESCh. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - Prob. 5ESCh. 12.1 - Prob. 6ESCh. 12.1 - Prob. 7ESCh. 12.1 - Prob. 8ESCh. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - Prob. 10ESCh. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - Prob. 12ESCh. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - Prob. 14ESCh. 12.1 - Prob. 15ESCh. 12.1 - Prob. 16ESCh. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - Prob. 18ESCh. 12.1 - Prob. 19ESCh. 12.1 - Prob. 20ESCh. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - Prob. 22ESCh. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - Prob. 24ESCh. 12.1 - Prob. 25ESCh. 12.1 - Prob. 26ESCh. 12.1 - In 25—27, find a regular expression that defines...Ch. 12.1 - Let r, s, and t be regular expressions over...Ch. 12.1 - Prob. 29ESCh. 12.1 - Prob. 30ESCh. 12.1 - Prob. 31ESCh. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - Prob. 33ESCh. 12.1 - Prob. 34ESCh. 12.1 - Prob. 35ESCh. 12.1 - Prob. 36ESCh. 12.1 - Prob. 37ESCh. 12.1 - Prob. 38ESCh. 12.1 - Prob. 39ESCh. 12.1 - Prob. 40ESCh. 12.1 - Write a regular expression to define the set of...Ch. 12.2 - The five objects that make up a finite-state...Ch. 12.2 - The next-state table for an automaton shows the...Ch. 12.2 - In the annotated next-state table, the initial...Ch. 12.2 - A string w consisting of input symbols is accepted...Ch. 12.2 - The language accepted by a finite-state automaton...Ch. 12.2 - If N is the next-stale function for a finite-state...Ch. 12.2 - One part of Kleene’s theorem says that given any...Ch. 12.2 - The second part of Kleene’s theorem says that...Ch. 12.2 - A regular language is .__________Ch. 12.2 - Given the language consisting of all strings of...Ch. 12.2 - Find the state of the vending machine in Example...Ch. 12.2 - Prob. 2ESCh. 12.2 - Prob. 3ESCh. 12.2 - Prob. 4ESCh. 12.2 - Prob. 5ESCh. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 8 and 9, a finite-state automaton is given by...Ch. 12.2 - In 8 and 9, a finite-state automaton is given by...Ch. 12.2 - A finite-state automaton A given by the transition...Ch. 12.2 - A finite-state automaton A given by the transition...Ch. 12.2 - Prob. 12ESCh. 12.2 - Consider again the finite-state automaton of...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - Prob. 15ESCh. 12.2 - Prob. 16ESCh. 12.2 - Prob. 17ESCh. 12.2 - Prob. 18ESCh. 12.2 - Prob. 19ESCh. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - Prob. 21ESCh. 12.2 - Prob. 22ESCh. 12.2 - Prob. 23ESCh. 12.2 - Prob. 24ESCh. 12.2 - Prob. 25ESCh. 12.2 - Prob. 26ESCh. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - Prob. 28ESCh. 12.2 - Prob. 29ESCh. 12.2 - Prob. 30ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 32ESCh. 12.2 - Prob. 33ESCh. 12.2 - Prob. 34ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 36ESCh. 12.2 - Prob. 37ESCh. 12.2 - Prob. 38ESCh. 12.2 - Prob. 39ESCh. 12.2 - Prob. 40ESCh. 12.2 - Prob. 41ESCh. 12.2 - Prob. 42ESCh. 12.2 - Prob. 43ESCh. 12.2 - Prob. 44ESCh. 12.2 - Prob. 45ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 47ESCh. 12.2 - Prob. 48ESCh. 12.2 - Write a computer algorithm that simulates the...Ch. 12.2 - Prob. 50ESCh. 12.2 - Prob. 51ESCh. 12.2 - Prob. 52ESCh. 12.2 - Prob. 53ESCh. 12.2 - a. Let A be a finite-state automaton with input...Ch. 12.3 - Given a finite-state automaton A with...Ch. 12.3 - Prob. 2TYCh. 12.3 - Given states s and t in a finite-state automaton...Ch. 12.3 - Prob. 4TYCh. 12.3 - Prob. 5TYCh. 12.3 - Consider the finite-state automaton A given by the...Ch. 12.3 - Consider the finite-state automaton A given by the...Ch. 12.3 - Consider the finite-state automaon A discussed in...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Prob. 7ESCh. 12.3 - Prob. 8ESCh. 12.3 - Prob. 9ESCh. 12.3 - Prob. 10ESCh. 12.3 - Prob. 11ESCh. 12.3 - Prob. 12ESCh. 12.3 - Prob. 13ESCh. 12.3 - Prob. 14ESCh. 12.3 - Prob. 15ESCh. 12.3 - Prob. 16ESCh. 12.3 - Prob. 17ESCh. 12.3 - Prob. 18ES
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- Using Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates). HINT: Pay closeattention to both the 1’s and the 0’s of the function.arrow_forwardRecall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forwardTheorem 1: A number n ∈ N is divisible by 3 if and only if when n is writtenin base 10 the sum of its digits is divisible by 3. As an example, 132 is divisible by 3 and 1 + 3 + 2 is divisible by 3.1. Prove Theorem 1 2. Using Theorem 1 construct an NFA over the alphabet Σ = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}which recognizes the language {w ∈ Σ^(∗)| w = 3k, k ∈ N}.arrow_forward
- Recall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forwardFind the sum of products expansion of the function F(x, y, z) = ¯x · y + x · z in two ways: (i) using a table; and (ii) using Boolean identities.arrow_forwardGive both a machine-level description (i.e., step-by-step description in words) and a state-diagram for a Turing machine that accepts all words over the alphabet {a, b} where the number of a’s is greater than or equal to the number of b’s.arrow_forward
- Compute (7^ (25)) mod 11 via the algorithm for modular exponentiation.arrow_forwardProve that the sum of the degrees in the interior angles of any convex polygon with n ≥ 3 sides is (n − 2) · 180. For the base case, you must prove that a triangle has angles summing to 180 degrees. You are permitted to use thefact when two parallel lines are cut by a transversal that corresponding angles are equal.arrow_forwardAnswer the following questions about rational and irrational numbers.1. Prove or disprove: If a and b are rational numbers then a^b is rational.2. Prove or disprove: If a and b are irrational numbers then a^b is irrational.arrow_forward
- Prove the following using structural induction: For any rooted binary tree T the number of vertices |T| in T satisfies the inequality |T| ≤ (2^ (height(T)+1)) − 1.arrow_forward(a) Prove that if p is a prime number and p|k^2 for some integer k then p|k.(b) Using Part (a), prove or disprove: √3 ∈ Q.arrow_forwardProvide a context-free grammar for the language {a^ (i) b^ (j) c^ (k) | i, j, k ∈ N, i = j or i = k}. Briefly explain (no formal proof needed) why your context-free grammar is correct and show that it produces the word aaabbccc.arrow_forward
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