Math

Discrete Mathematics With Applicationsa. Let A be a finite-state automaton with input alphabet ∑ , and suppose L ( A ) is the language accepted by A. The complement of L ( A ) is the set of all strings over ∑ that are not in L ( A ) . Show that the complement of a regular language is regular by proving the following: L ( A ) is the language accepted by a finite-state automaton A, then there is a finite-state automaton A ′ that accepts the complement of L ( A ) . b. Show that the intersection of any two regular languages is regular as follows: First prove that if L ( A 1 ) and L ( A 2 ) are languages accepted by automata A 1 and A 2 , respectively, then there is an automaton A that accepts ( L ( A 1 ) ) c ∪ ( A ( A 2 ) ) c . Then use one of Dc Morgan’s laws for sets, the double complement law for sets, and the result of part (a) to prove that there is an automaton that accepts L ( A 1 ) ∩ L ( A 2 ) .BuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 12.2, Problem 54ES

Textbook Problem

a. Let *A *be a finite-state automaton with input alphabet
*A. *The complement of
*. *Show that the complement of a regular language is regular by proving the following:
*A, *then there is a finite-state automaton
*. *

b. Show that the intersection of any two regular languages is regular as follows: First prove that if
*, *respectively, then there is an automaton *A *that accepts
*. *Then use one of Dc Morgan’s laws for sets, the double complement law for sets, and the result of part (a) to prove that there is an automaton that accepts

Discrete Mathematics With Applications

Show all chapter solutions

Ch. 12.1 - If x and y are strings, the concatenation of x and...Ch. 12.1 - If L and Lare languages, the Concatenation of L...Ch. 12.1 - If L and Lare languages, the union of L and L is...Ch. 12.1 - If L is a language, the Kleene closure of L is...Ch. 12.1 - The set of regular expressions over an alphabet is...Ch. 12.1 - The function that associates a language to each...Ch. 12.1 - The notation [A-C] is an example of a____ and...Ch. 12.1 - Use of a single dot in a regular expression stands...Ch. 12.1 - The symbol ^, placed at the beginning of a...Ch. 12.1 - If r is a regular expression, the notation r +...

Ch. 12.1 - If r is a regular expression, the notation...Ch. 12.1 - If r is a regular expression, the notation r{n}...Ch. 12.1 - In 1 and 2, let={x,y} be an alphabet. 1. a. Let...Ch. 12.1 - In 1 and 2, let={x,y} be an alphabet. 2. a. Let L3...Ch. 12.1 - If the expression ab+cd+ in postfix notation is...Ch. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - In 25—27, find a regular expression that defines...Ch. 12.1 - In 25—27, find a regular expression that defines...Ch. 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 - Let r, s, and t be regular expressions over...Ch. 12.1 - Let r, s, and t be regular expressions over...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - Write a regular expression to perform a complete...Ch. 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 - 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 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 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 - Consider again the finite-state automaton of...Ch. 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 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - A simplified telephone switching system allows the...Ch. 12.2 - Write a computer algorithm that simulates the...Ch. 12.2 - Write a computer algorithm that simulates the act...Ch. 12.2 - Let L be the language consisting of all strings of...Ch. 12.2 - Let L be the language consisting of all strings of...Ch. 12.2 - Let L be the language consisting of all strings of...Ch. 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 - Given a finite-state automaton A with...Ch. 12.3 - Given states s and t in a finite-state automaton...Ch. 12.3 - If A is a finite-state automaton, then for some...Ch. 12.3 - Given a finite-state automaton A, the set of...Ch. 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 - Are the automata A and A’ shown below equivalent?Ch. 12.3 - Are the automata A and A’ shown below equivalent?Ch. 12.3 - Are the automata A and A’ shown below equivalent?Ch. 12.3 - Are the automata A and A’ shown below equivalent?Ch. 12.3 - Prove property (12.3.1).Ch. 12.3 - How should the proof of property (12.3.1) be...Ch. 12.3 - Prove property (12.3.3).Ch. 12.3 - Prove property (12.3.4).Ch. 12.3 - Prove property (12.3.5).Ch. 12.3 - Prove property (12.3.6).Ch. 12.3 - Prove that if two states of a finite-state...Ch. 12.3 - Write a complete proof of property (12.3.7).

Find more solutions based on key concepts

Show solutions In Exercises 2330, factor each expression and simplify as much as possible. (x2+1)x+1(x+1)3

Finite Mathematics

In Problems 21 and 22, use tables to investigate each limit. Check your result analytically or graphically.
22....

Mathematical Applications for the Management, Life, and Social Sciences

Express the following hexadecimal numbers as decimal numbers. a. C216 b. 5B16 c. A20D16 d. 17E316

Mathematics For Machine Technology

In Exercises 730, solve each linear programming problem by the method of corners. Minimize C=5x+3y subject to t...

Finite Mathematics for the Managerial, Life, and Social Sciences

Genotypes The eye color of mice is determined by a dominant allele E. corresponding to black eyes, and a recess...

Mathematical Excursions (MindTap Course List)

A cable runs from the top of a building to a point on the ground 66.5 feet from the base of the building. If th...

Mathematics: A Practical Odyssey

59.45 is 41% of what number?

Elementary Technical Mathematics

A production line operation is designed to fill cartons with laundry detergent to a meanweight of 32 ounces. A ...

Essentials Of Statistics For Business & Economics

For the line l:x,y,z=2,3,4+n3,-2,5, find a a point of the line. b a direction vector for the line.

Elementary Geometry for College Students

Finding an Equation for a Surface of RevolutionIn Exercises 3136, find an equation for the surface of revolutio...

Multivariable Calculus

Finding or Evaluating an Integral In Exercises 5562, find or evaluate the integral. sin1+cos2d

Calculus (MindTap Course List)

Is it possible to obtain a negative value for the variance or the standard deviation?

Statistics for The Behavioral Sciences (MindTap Course List)

Prove that every ideal in where is a field, is a principal ideal.

Elements Of Modern Algebra

In Exercises 1-4, use the graph of the function f to find approximations of the given values. a. f(2) b. f(0) c...

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 98-102, determine whether the statement is true or false. If it is tine, explain why it is tine. I...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

a What is true of any pair of corresponding angles of two similar polygons? b What is true of any pairs of corr...

Elementary Geometry For College Students, 7e

Find an equation for the conic that satisfies the given conditions. 41. Ellipse, center (1, 4), vertex (1,0), f...

Single Variable Calculus: Early Transcendentals

True or False:
is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

Let X represent the error in making a measurement of a physical characteristic or property (e.g., the boiling p...

Probability and Statistics for Engineering and the Sciences

Using Double- or Half-Angle Formulas Use a Double- or Half-Angle Formula to solve the equation in the interval ...

Precalculus: Mathematics for Calculus (Standalone Book)

Logarithmic Differentiation In Exercises 19 and 20, use logarithmic differentiation to find dy/dx. y=x+23x2,x23

Calculus of a Single Variable

Childhood participation in sports, cultural groups, and youth groups appears to be related to improved selfeste...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Young Adult magazine states the following hypotheses about the mean age of its subscribers. H0: = 28 Ha: 28 ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Please provide the following information for Problems 11-22. (a) What is the level of significance? State the n...

Understanding Basic Statistics

For Problems 1-50, solve each equation. Objective 1 3(x+2)=3x+6

Intermediate Algebra

The graph of the acceleration a(t) of a car measured in ft/s2 is shown. Use the Midpoint Rule to estimate the i...

Calculus (MindTap Course List)

Find the limit. Use lHospitals Rule where appropriate. If there is a more elementary method, consider using it....

Single Variable Calculus: Early Transcendentals, Volume I

Explain why partial counterbalancing is sometimes necessary.

Research Methods for the Behavioral Sciences (MindTap Course List)

Divergence and Curl In Exercises 19-26, find (a) the divergence of the vector field and (b) the curl of the vec...

Calculus: Early Transcendental Functions (MindTap Course List)

Political Fundraiser A politician raises funds by selling tickets to a dinner for $500. The politician pays $15...

Calculus: An Applied Approach (MindTap Course List)

This exercise requires the use of a statistical software package. The cotton aphid poses a threat to cotton cro...

Introduction To Statistics And Data Analysis

Practice with Exponents Problems A-1 through A-5 provide practice with the basic rules for exponents. In each c...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Evaluate the integral 0101emaxx2,y2dydxwhere max{x2, y2} means the larger of the numbers x2 and y2.

Multivariable Calculus

a. SW Statewide, social workers average 10.2 years of experience. In a random sample, 203 social workers in gre...

Essentials Of Statistics

Comet Hale-Bopp The comet Hale-Bopp has an elliptical orbit with the sun a, one focus and has an eccentricity o...

Calculus: Early Transcendental Functions

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Applied Calculus

The figure shows the graph of the derivative f of a function f. (a) On what intervals is f increasing or decrea...

Single Variable Calculus

Practice Write each number or expression without using exponents. 4x3

College Algebra (MindTap Course List)

The American Community Survey showed that residents of New York City have the longest travel times to get to wo...

Statistics for Business & Economics, Revised (MindTap Course List)

Describe the purpose and responsibilities of the Institutional Animal Care and Use Committee (IACUC).

Research Methods for the Behavioral Sciences (MindTap Course List)

Sometimes, Always, or Never:
If c is a critical number, then f′(c) = 0.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

For the following statements, underline the key words and translate into equations.
16. The cost of Q at $4.55 ...

Contemporary Mathematics for Business & Consumers

Solve each equation for x. 54. (a) ln(ln x) = 1 (b) eax = Cebx, where a b

Calculus: Early Transcendentals

Use your graphing calculator to convert the complex number to trigonometric form in the following problems. Pro...

Trigonometry (MindTap Course List)

True or False: Every separable first-order equation dy/dx = g(x)h(y) is exact.

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

For the following exercises, for each linear equation, a. give the slope m and y -intercept b, if any, and b. g...

Calculus Volume 1

In the following exercises, use the Fundamental Theorem of Calculus, Part 1, to find each derivative. 149. ddx1...

Calculus Volume 2

Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 in...

Introductory Statistics

The pursuit of a higher education degree in business is now international. A survey shows that more and more As...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)