/*! 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} Q27E Read the informal definition of ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Log out

Learning Materials

Features

Discover

Chapter 0: Q27E (page 1)

Read the informal definition of the finite state transducer given in Exercise 1.24. Give the state diagram of an FST with the following behaviour. Its input and output alphabets are 0,1 . Its output string is identical to the input string on the even positions but inverted on the odd positions. For example, on input 0000111 it should output 1010010 .

Short Answer

Expert verified

In even positions output string is same as input string

In odd positions, output string is inverted

Step by step solution

01

Introduction 

Given alphabets for FST are 0,1. It has the following behavior

Its output string is identical to the input string on the even positions.

Its output string is inverted on the odd positions.

So that the state diagram of that FST is

02

Explanation 

So, by this state diagram,

In even positions output string is same as input string

i.e. for input 0→output is also 0

for input 1→output is also 1

In odd positions, output string is inverted

i.e. for input 0→output is 1

for input 1→output is 0.

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 91Ó°ÊÓ!

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

Question: Each of the following languages is the intersection of two simpler languages. In each part, construct DFAs for the simpler languages, then combine them using the construction discussed in footnote 3 (page 46) to give the state diagram of a DFA for the language given. In all parts,∑=a,b.

a.{w|w\kern1pt has  at  least  three  a's  and  at  least  two  b's}b.w|w\kern1pt has  exactly  two  a's  and  at  least  two  b'sc.w|w\kern1pt has  even number  of  a's  and  one or  two  b'sd.{w|w\kern1pt has  even number  of  a's  and eachais followed by at least  one b}e.w|w\kern1pt starts  with  an  a  and  has at most one  bf.w|w\kern1pt has an odd number ofa's  and ends with a  bg.w|w\kern1pt has even length and an odd number ofa's

LetAbe the set{x,y,z}andBbe the set{x,y}.

  1. IsAa subset ofB?
  2. IsBa subset ofA?
  3. What isA∪B?
  4. What isA∩B?
  5. What isA×B?
  6. What is the power set ofB ?

Let

∑3=000,001,010,----,111

∑3contains all size 3 columns of 0s and 1 s. A string of symbols in∑3gives three rows of 0s and 1s. Consider each row to be a binary number and let B=W∈∑*3the bottom row of W is the sum of the top two rows}.

For example,

001,100,010,110∈Bbut001,101∉B

Show that Bis regular.

(Hint: Working with BRis easier. You may assume the result claimed in Problem 1.31.)

Question: Each of the following languages is the complement of a simpler language. In each part, construct a DFA for the simpler language, and then use it to give the state diagram of a DFA for the language given. In all parts, Σ=a,b.

a.w|wdoesnotcontainthesubstringabAb.{w|wdoesnotcontainthesubstringbaba}c.{w|wcontainsneitherthesubstringsabnorba}d.{w|wisanystringnotina*b*}e.{w|wisanystringnotin(ab+)*}f.{w|wisanystringnotina*∪b*}g.{w|wisanystringthatdoesntcontainexactlytwoas}h.{w|wisanystringexceptaandb}

Use the procedure described in Lemma 1.60to convert the following finite automata to regular expressions.

See all solutions

Recommended explanations on Computer Science Textbooks

Data Structures

Read Explanation

Computer Organisation and Architecture

Read Explanation

Computer Network

Read Explanation

Game Design in Computer Science

Read Explanation

Computer Systems

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.