A bit-string is simply a finite sequence of zeroes and ones. For the purposes of this problem, strings will always have length >= 1, i.e. no zero-length strings.

anudoneddbv 2022-07-18 Answered
Discrete Math Recursive Definition
A bit-string is simply a finite sequence of zeroes and ones. For the purposes of this problem, strings will always have length 1, i.e. no zero-length strings.
Let A n be the number of strings of length n that have no two consecutive zeros. Thus A 1 = 2 and A 2 = 3 (strings 01, 10 and 11).
Give recursive definitions for A n .
My Answer:
A ( n + 1 ) = A ( n ) + A ( n 1 ) ,
A ( n ) = A ( n 1 ) + A ( n 2 ) .
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Answers (1)

Danica Ray
Answered 2022-07-19 Author has 15 answers
Step 1
I assume A n to be the actual sets not just their respective size.
Step 2
A n + 2 equals the disjoint union of the set X of sequences ending in 1 and the set Y of sequences ending in 10. A n + 1 maps bijectively on X via ( x 1 , , x n + 1 ) ( x 1 , , x n + 1 , 1 ) and A n on Y via ( x 1 , , x n ) ( x 1 , , x n , 1 , 0 ).
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