9. A computer system considers a string of the digits 0, 1, 2, 3 a valid codeword if it has no two consecutive 1's. For example 01213 is a valid codeword of length 5 while 11320, 1022110, and 211133 are not valid. Let a, be the number of valid codewords of length n. Find a recurrence relation for a, and hence use it to find as.

In recurrence relation T(n) = T(n/3)+Θ(n2), the number of sub-problems are a 2 b n/2 c 1 d 3

11) Let b, be the number of binary sequences of length n that have no consecutive 0's. a) List the binary sequences for n = 1,2,3,4 b) Give a recurrence relation for b, .

Let T(n) be defined by the first-order linear recurrence T(n) = 2T(n-1) +8 Suppose it is given that T(2) = c. Compute T(0) by iterating backwards and express your answer in terms of c. T(0) =

Prove using the concept of interpretations and the value of a formula vI under an interpretation I that
[∀x p(x) ∨ ∃x q(x)] → ∃x[p(x) ∨ q(x)] is valid.

Develop a closed form solution for the recurrence relation: P(n) = 5 if n = 0, P(n) = P(n-1)+3 if n > 0 Prove the closed form solution is valid for all n

Find the solution for each of the following recurrences, and then give tight bounds (i.e., in Θ(·)) for T (n). (a) T (n) = T (n − 1) + 1/n with T (0) = 0. (b) T (n) = T (n − 1) + cn with T (0) = 1, where c > 1 is some constant (c) T (n) = 2 T (n − 1) + 1 with T (0) = 1

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Use resolution to show Vx Vy[p(x, y) → ¬p(y, x)] F ¬p(x, x)

Hello, Can you please help me with this problem because I don't understand how to do this problem can you please do it step by step and can you explain it in full detail on answer this question. Thank you.

We are given a recurrence of T(n) = T(n-1) + (n). For this recurrence it must be proven that T(n) is C (n^2).