3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings...
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.) Let z be the number of binary strings of length n that do not contain the substring 000 Find a recurrence relation for z You are not required to find a closed form for this recurrence Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.)...
Discrete Mathematics 7. (15 points) Let an be the number of length n ({ne Zin 20}) ternary strings (strings made up of {0, 1, 2), ex. 01211120002) that contain two consecutive digits that are the same. For example, a = 3 since the only ternary strings of length 2 with matching consecutive digits are 00, 11, and 22. Also, a, = 0, since in order to have consecutive matching digits, a string must be of length at least two. a....
Give a recursive formula for the function g(n) that counts the number of ternary strings of length n that do not contain 2002 as a substring. You do not need to find a closed form solution for g(n).
Discrete math 4. Popeye and Olive Oyl frequently send each other text messages that are just contiguous strings of the three emojis , , and . For instance, one particular length-5 emoji string might be e (a) Find a recurrence relation for the number of possible length-n emoji strings that do not contain two consecutive winkey emojis, (b) What are the initial conditions for the recurrence relation? (c) Find a closed-form solution to the recurrence relation you found in part...
1. Call a string of lettes ega if i can be produced by concatenating (running together) copies of the strings 'a, 'b','c' and 'ddd. For example, the string 'act' is legal because it can be produced by concatenating 'a', 'cc' and b', but the string 'ccca' is not legal. For each integer n 2 1, let tn be the number of legal strings with n letters. For example, 1-2 (a' and 'b' are the legal strings). (a) Write down t2...
6. (10 points) Let Sn be the number of n-bit strings of O's and 1's that avoid the pattern "11". Find the recurrence relation for sm and find the solution for this recurrence relation.
1. Call a string of letters "legal if it can be produced by concatenating (running together) copies of the strings 'a', 'b', 'cc' and 'ddd'. For example, the string 'accb' is legal because it can be produced by concatenating 'a', 'cc' and 'b', but the string 'ccca' is not legal. For each integer n 21, let tn be the number of legal strings with n letters. For example, t1 2 (a and 'b' are the legal strings) (a) Write down...
3. Let Tn(x) be the degree n Chebyshev polynomial. Evaluate Tn (0.5) for 2 <n < 10, by applying the three-term recurrence directly with x = 0.5, starting with T.(0.5) = 1 and Ti(0.5) = 0.5.
This is discrete mathematics. 1. 5 points] Let T be the set of strings whose alphabet is 10, 1,2,3) such that, in every element of T a. Every 1 is followed immediately by exactly one 0. b. Every 2 is followed immediately by exactly two 0s. c. Every 3 is followed immediately by exactly three 0s. For instance, 00103000 E T.) Find a recursive definition for T 1. 5 points] Let T be the set of strings whose alphabet is...
explain why the recurrence relation for number of ternary strings of length n contains "01" 7. (10 points) Extra credit: Explain why the recurrence relation for number of ternary strings of length n that contain "01" is bn = 3n-1-bn-2 +31-2?