   Chapter 9.3, Problem 26ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Counting Strings: Consider the set of all string of a ' s ,   b ' s , and c ' s . Make a list of all of these string of lengths 0, 1, 2, and 3 that do not contain the pattern aa. For each integer n ≥ 0 , let s n = the number of strings of a ' s , ​   b ' s , and c ' s of length n that do not contain the pattern aa. Find s 0 ,   s 1 ,   s 2 , and s 3 ,   .... Find a recurrence relation for s 0 ,   s 1 ,   s 2 ,   .... Use the results of parts (b) and (c) to find the number of strings of a ' s ,   b ' s , and c ' s of length four that do not contain the pattern aa. Use the technique described in Section 5.8 to find an explicit formula for s 0 ,   s 1 ,   s 2 ,   ...

To determine

(a)

To make a list of all bit strings of lengths 0,1,2,3 and 4 and that don’t contain the bit pattern 111

Explanation

Given information:

Bit strings of binary containing the two bits 0 and 1.

Calculation:

The bit strings of length 0 that don’t contain 111 =0.

The bit strings of length 1 that don’t contain 111 =0,1

To determine

(b)

To find the value of d1, d2

d3 and d4

To determine

(c)

To find the recurrence relation for d1, d2

d3 and d4.

To determine

(d)

To find the number of bit strings of length 5 that do not contain the bit pattern 111.

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