Introduction to Theory of Computation

Michael Sipser

Computer Science

3rd Edition 路 458 pages

ISBN: 9781133187790

Chapter 1: Q31P (page 88)

For any string $w = w_{1}, w_{2}, 路路路, w_{n}$ , the reverse of w, written wR , is the string w in reverse order, $w_{n} 路路路 w_{2} w_{1}$ . For any language $A, let AR = \{wR | w A\} .$ Show that if A is regular, so is AR.

Short Answer

Expert verified

It means that $w 鈭� A$ if $w^{R} 鈭� A^{R}$

Step by step solution

To Convert the state for M

It recognizes A,

We have built a NFA for as follows:

Convert the start state for M as the only accept state $q_{a c c e p t}^{'}$ for $M'$ .

Add a new start state $q_{o}^{'}$ for $M'$ , and from $q_{o}^{'}$ , add $鈭� -$ transitions to $M'$ each state of corresponding to accept states of M.

To Accept the State M

Here $q_{o}^{'} = q_{a c c e p t}^{'}$

For any $w 鈭� 鈭� *$ there is a path following w from the start state to an accept sate in M if there is a path following $w^{R}$ from $q_{o}^{'}$ to $q_{a c c e p t}^{'}$ in $M'$

That means that $w 鈭� A$ if $w^{R} 鈭� A^{R}$ .

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91影视

For any string $w = w_{1}, w_{2}, 路路路, w_{n}$ , the reverse of w, written wR , is the string w in reverse order, $w_{n} 路路路 w_{2} w_{1}$ . For any language $A, let AR = \{wR | w A\} .$ Show that if A is regular, so is AR.

Short Answer

Step by step solution

To Convert the state for M

To Accept the State M

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

91影视

For any string w=w1,w2,路路路,wn, the reverse of w, written wR , is the string w in reverse order,wn路路路w2w1. For any language A,letAR=wR|wA.Show that if A is regular, so is AR.

Short Answer

Step by step solution

To Convert the state for M

To Accept the State M

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Data Structures

Issues in Computer Science

Theory of Computation

Big Data

Functional Programming

Problem Solving Techniques

Study anywhere. Anytime. Across all devices.

For any string $w = w_{1}, w_{2}, 路路路, w_{n}$ , the reverse of w, written wR , is the string w in reverse order, $w_{n} 路路路 w_{2} w_{1}$ . For any language $A, let AR = \{wR | w A\} .$ Show that if A is regular, so is AR.