Problem 3: We want to create a string of length n from the following blocks of letters: A, B, T K, CC, DD, EE. (a) Let P, denote the number of such blocks. For example, AAAB, ABEE and DDCC are blocks of length 4. Set up and justify the recurrence for P. (Make sure to provide the initial conditions). (b) Let T₁ denote the number of such words, in which blocks A and CC can't be next to each other (no ACC or CCA), no three A's and no two blocks of CC's in a row (no AAA or CCCC). For example, ABCCDD and CCEEEE are valid strings of length 6, while CCBAAA, BCCABB and CCCCDD are not. Set up and justify the recurrence for T How many initial conditions do you need to know in order to solve the recurrence? Give only the first two initial conditions.

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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Problem 3: We want to create a string of length n from the following blocks of letters: A,
B, TK, CC, DD, EE.
(a) Let P₁ denote the number of such blocks. For example, AAAB, ABEE and DDCC
are blocks of length 4. Set up and justify the recurrence for Pn. (Make sure to provide the
initial conditions).
(b) Let T₁ denote the number of such words, in which blocks A and CC can't be next to
each other (no ACC or CCA), no three A's and no two blocks of CC's in a row (no AAA
or CCCC). For example, ABCCDD and CCEEEE are valid strings of length 6, while
CCBAAA, BCCABB and CCCCDD are not. Set up and justify the recurrence for T
How many initial conditions do you need to know in order to solve the recurrence? Give
only the first two initial conditions.
Transcribed Image Text:Problem 3: We want to create a string of length n from the following blocks of letters: A, B, TK, CC, DD, EE. (a) Let P₁ denote the number of such blocks. For example, AAAB, ABEE and DDCC are blocks of length 4. Set up and justify the recurrence for Pn. (Make sure to provide the initial conditions). (b) Let T₁ denote the number of such words, in which blocks A and CC can't be next to each other (no ACC or CCA), no three A's and no two blocks of CC's in a row (no AAA or CCCC). For example, ABCCDD and CCEEEE are valid strings of length 6, while CCBAAA, BCCABB and CCCCDD are not. Set up and justify the recurrence for T How many initial conditions do you need to know in order to solve the recurrence? Give only the first two initial conditions.
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