Chapter 1: Q31P (page 88)

For any string $w = w_{1}, w_{2}, \cdot \cdot \cdot, w_{n}$ , the reverse of w, written wR , is the string w in reverse order, $w_{n} \cdot \cdot \cdot w_{2} w_{1}$ . 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 $w \in A$ if $w^{R} \in A^{R}$

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 $\in -$ 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 $w \in \sum *$ 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 $w \in A$ if $w^{R} \in A^{R}$ .

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For any string $w = w_{1}, w_{2}, \cdot \cdot \cdot, w_{n}$ , the reverse of w, written wR , is the string w in reverse order, $w_{n} \cdot \cdot \cdot w_{2} w_{1}$ . 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.

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For any string w=w1,w2,···,wn, the reverse of w, written wR , is the string w in reverse order,wn···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

Game Design in Computer Science

Computer Programming

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Study anywhere. Anytime. Across all devices.

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