/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q34P Let 危2聽be the same as in Probl... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q34P (page 89)

Let 危2be the same as in Problem 1.33. Consider each row to be a binary number and let D={w鈭�危*2|the top row of w is a larger number than is the bottom row}. For example, 00101100鈭�D, but 000111006鈭�D. How that D is regular.

Short Answer

Expert verified

Dis a regular language.

Step by step solution

01

Considering each has binary number

The Given language is D={w鈭�鈭�2*|

The top of w is the larger number than is the bottom row}

Over the alphabet is

The Language for given expression

Here each row has binary number.

02

Explanation

Let M be theDFA, over the input alphabet .

The state transition diagram ofM is as follows:

Prove that D is a regular language.

A language is said to be regular if it is recognized by a DFA.

Let take string form language,

Initial state of the aboveDFA is 鈥榚qual鈥�

Parse string

Here 鈥榣arge鈥� is final state , the string is accepted by the DFA.

Thus, language of given D is accepted by the given.

DFA to recognize the language D.

Therefore, D is a regular language.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The pumping lemma says that every regular language has a pumping length P , such that every string in the language can be pumped if it has length p or more. If P is a pumping length for language A, so is any length p'猢�pThe minimum pumping length for A is the smallest p that is a pumping length for A . For example, if A=01*, the minimum pumping length is 2.The reason is that the string s=0is in A and has length 1 yet s cannot be pumped; but any string A in of length 2 or more contains a 1 and hence can be pumped by dividing it so that x=0,y=1,andzis the rest. For each of the following languages, give the minimum pumping length and justify your answer.

a).0001*b).0*1*c).001鈭�0*1*d).0*1+0+1*鈭�10*1

role="math" localid="1660797009042" e).(01)*f).鈭�g).1*01*01*h).10(11*0)*

i).1011j).鈭�*

If A is a set of natural numbers and k is a natural number greater than 1, let

Bk(A)={w|wistherepresentationinbasekofsomenumberinA}.

Here, we do not allow leading 0s in the representation of a number. For example ,B2({3,5})={11,101}and B3({3,5})={10,12}.Give an example of a set A for which B2(A)is regular butB2(A) is not regular. Prove that your example works.

A finite state transducer (FST) is a type of deterministic finite automaton whose output is a string and not just accept or reject. The following are state diagrams of finite state transducers T1andT2.

Each transition of an FST is labeled with two symbols, one designating the input symbol for that transition and the other designating the output symbol. The two symbols are written with a slash, I, separating them. In T1, the transition from q1鈥�toq2has input symbol 2 and output symbol 1. Some transitions may have multiple input鈥搊utput pairs, such as the transition in T1from q1to itself. When an FST computes on an input string w, it takes the input symbols w1路路路wnone by one and, starting at the start state, follows the transitions by matching the input labels with the sequence of symbols w1路路路wn=w. Every time it goes along a transition, it outputs the corresponding output symbol. For example, on input 2212011, machine T1enters the sequence of states q1,q2,q2,q2,q2,q1,q1,q1and produces output 1111000. On input abbb, T2outputs 1011. Give the sequence of states entered and the output produced in each of the following parts.

a. T1on input011

b. T1on input211

c. T1on input121

d. T1on input0202

e. T2on input b

f. T2on input bbab

g. T2on input bbbbbb

h. T2on input localid="1663158267545" 蔚

a. Let Abe an infinite regular language. Prove thatA can be split into two infinite disjoint regular subsets.

b. LetBandD be two languages. Write B鈯�鈯�DifB鈯�Dand Dcontains infinitely many strings that are not in B. Show that if BandD are two regular languages whereB鈯�鈯�D , then we can find a regular languageC where B鈯�鈯�C鈯�鈯�D.

Let A/B={蝇|蝇鈥�蠂鈥�Aforsome蠂鈥�鈭�B}.Show that if is regular and is any language, thenA/B is regular.
See all solutions

Recommended explanations on Computer Science Textbooks

Computer Organisation and Architecture

Read Explanation

Data Representation in Computer Science

Read Explanation

Functional Programming

Read Explanation

Computer Network

Read Explanation

Cloud Services

Read Explanation

Databases

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.