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Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser
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Let 3 =nh0 0 0i,h0 0 1i,h0 1 0i,...,h1 1 1io. 3 contains

Chapter , Problem 1.32

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QUESTION:

Let 3 =nh0 0 0i,h0 0 1i,h0 1 0i,...,h1 1 1io. 3 contains all size 3 columns of 0s and 1s. A string of symbols in 3 gives three rows of 0s and 1s. Consider each row to be a binary number and letB = {w 3| the bottom row of w is the sum of the top two rows}.For example,h0 0 1ih1 0 0ih1 1 0i B, but h0 0 1ih1 0 1i6 B. Show that B is regular. (Hint: Working with BR is easier. You may assume the result claimed in 1.31.)

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QUESTION:

Let 3 =nh0 0 0i,h0 0 1i,h0 1 0i,...,h1 1 1io. 3 contains all size 3 columns of 0s and 1s. A string of symbols in 3 gives three rows of 0s and 1s. Consider each row to be a binary number and letB = {w 3| the bottom row of w is the sum of the top two rows}.For example,h0 0 1ih1 0 0ih1 1 0i B, but h0 0 1ih1 0 1i6 B. Show that B is regular. (Hint: Working with BR is easier. You may assume the result claimed in 1.31.)

ANSWER:

Step 1 of 2

 Given that, has a binary number in each row. And  is defined as the language of

.

To show is regular, let us consider that is regular. Then if   is regular  is regular by theorem, regular languages are close under regular.

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