Let A = {(N1, N2) | N1 and N2 are NFAS and L(N1)N L(N2) = Ø}. Show that A is %3D decidable.

Q: (a) ged(24, 54) = 6 (b) gcd(18,42) = 6 Now you try some: Answers (c) gcd(244, 354) = 2 (d) gcd(128,…

A: - We have to work with GCD of two numbers.

Q: Given that EuV k=1 to n k = n(n+1)/2, evaluate Euu k=1 to n (k+1)

A:

Q: Let T(n) = T(n-2)+2T([])+n, for all n and T(n) E N(n²). 2 3. T(1) = T(2) 1. Prove that T(n) E O(2")…

A: Explanation given in step 2

Q: Show that the recurrence equation (n-1)tn-1+(n-1)tn-2 t₁ = 0 t₂ = 1 can be written as tn =…

A: Solution of the given recurrence equation is:

Q: 3. Try to obtain a closed form for the following recurrence equation: if n 4. |

A: Given p0 = 1 p1 = 1 p2 = 1 p3 = 3 p4 = p3 + (4-1)p2 - p1 + p0        = 3+3*1-1+1  = 6 p5= p4+ 4p3-…

Q: Compute in GF(28): (x4+x3+x2+1)/(x7+x5+x3+x2+1) where the irreducible polynomial is the one used in…

A:

Q: Let p(n) = Σa;n², i=0 where ad > 0, be a degree-d polynomial in n, and let k be a constant. Use the…

A: SOLUTION - We need to find for, If K > d, then p(n) = o(n)k

Q: Simplify the following in product of .3 sums (F(A,B,C,D) = (4,6,7,8,10,15 %3D (A+B'+D) + (B'+C'+D')…

A: Given that F(A,B,C,D) = π(4,6,7,8,10,15)  Product of sums

Q: Let T(n)T(n) be defined by the first-order linear recurrenceT(n)=5T(n−1)+3T(n)=5T(n−1)+3Suppose it…

A:

Q: Let U {0, 1, 2, ...,9}, A = {0, 3, 5, 8}, B = {0,1,2, 3, 6}, and C = {2,3,5, 8, 9}. AUBUC= AU (Bn C)…

A: We are given A universal set U, and other 3 sets A, B and C. We are going to perform given…

Q: Suppose f(n) = 19n³ and h(n) = 20n³ + n+ 23. Prove or disprove whether f(n) E N(h(n)) %3D Use the…

A: Here, we have to prove or disprove whether f(n) belongs to Ω(h(n)). As per the definition of Big…

Q: Demonstrate that n! equals O (nn).

A: According to the information given:- We have to prove n!=O(nn)

Q: More Examples • For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is…

A: In d part, we have to check f(n) is greater or equal than g(n) or not. Big-Omega(Ω) notation gives…

Q: Consider T(n)=T((n-1)/2) +2. Master Theorem can be used to solve this recurrence. Select one: O True…

A: We know master theorem : T(n)=aT(n/b)+ f(n) if a>=1 and b>=1 so we can use master method.   so…

Q: Convert  (111) 2 = (__) 10

A: Here is the detailed and simplified answer to the above listed problem statement:

Q: Express F as product of maxterms: F(a,b,c) = (a+b)c

A: Let's try to solve all the given options and see the result:

Q: Suppose that f(n) satisfies the divide-and-conquer recurrence relation f(n) = 3f(n/4)+n2/8 with f(1)…

A: A recurrence relation is an equation that defines a sequence recursively. That is, the terms of the…

Q: [o o 1 1 1 0 ] 3) If H = |1 0 0 1 1 1 0 is a parity check matrix for a linear code, then list all…

A:

Q: Prove that E is not regular E = { (₁01m 1n | m, n E IN₁ m2 man nz n}

A: - We have to see if the lnguage is regular or not.

Q: Show that {0"1m2* | k divides n + m} is not regular.

A: Introduction:  Regular Language: The set of regular languages over an alphabet ∑ is defined…

Q: create a truth table for a. (p^q) V~q b. r =>(p V q)

A: In a truth table, each row corresponds to a specific combination of truth values assigned to the…

Q: Determine if ∀a, b ∈ N, f(n) = a^n , g(n) = b^n , then it follows that f ∈ Θ(g).

A: f(n)=a^n g(n)=b^n Given a,b∈ N where a,b>0 Let k∈ N  such that a<=kb a^n<=(kb)^n

Q: make an adjacency matrix for the following: E= {(1,2),(2,1),(3,2),(4,3),(4,5),(5,6),(6,7)}

A: In this question we have to construct a adjacency matrix program a given graph set  Let's design a…

Q: If set A has size m, and set B has size n, then what is the size of the cross product of A and B?…

A: Introduction: A set is a collection of distinct and well-defined objects, which can be numbers,…

Q: Use the pumping lemma to prove the following language is nonregular: L = {a^nb^3^n} = {abbb,…

A: Pumping lemma is a fundamental device within the principle of formal languages, used to illustrate…

Q: Consider f(n) = 3n^2+2n-1, mathematically show that f(n) is O(n²), (n²), and O(n²).

A: a) answer:  f(n) = O(g(n)) means there are positive constants c and n0, such that 0 ≤ f(n) ≤ cg(n)…

Q: Let d p(n) = [a¡n', i=0 where ad > 0, be a degree-d polynomial in n, and let k be a constant. Use…

A: SOLUTION -   e. If k <d, then p(n) = w(nk).     Below I have added the image of the solution -…

Q: Given the following recurrence, find the growth rate of T(n): T(n) = 4T (n/2) + 6n³ with 7(1) = 0(1)

A: Introduction Master method: The master theorem for divide-and-conquer recurrences in algorithmic…

Q: or n=5 , In base there are more than 5 stars, however it should be equal to 5 like I shared picture…

A: In this question we have to write a python program for the hollow triangle with a same number of all…

Q: A) Prove the following by induction, substitution, or by definition that 5n²-n+1=(n) Definition of…

A: In this question we have to prove, using the definition of Big Theta (Θ), that the function 5n^2 - n…

Q: Let ENFA = {N | N is an NFA and L(N) = Ø}. Prove that ENFA is in P.

A: Ans

Q: Let B = {a + bi|a, b ∈ N}. Prove that B is countable.

A: Let B = {a + bi|a, b ∈ N}. Prove that B is countable. Theorem 2.3: handout on the cardinality and…

Q: 1. Prove that 1 i log i = O(n² log n). i=1

A: - We need to work on the expression of complexity.

Q: Prove that f1 + f3 + ⋯ + f2n−1 = f2n when n is a positive integer

A: Here this theorem is part of the Fibonacci series. The statement of this theorem is given below:…

Q: Consider the same house rent prediction problem where you are supposed to predict price of a house…

A: The solution to the above question is:

Q: 3. Let the "Tribonacci sequence" be defined by T₁ = T₂ = T₁=1 and T₁ = T₁+T2+T-3 for n ≥4. Prove…

A: A Tribonacci sequence or series is a sequence of integers such that each term from the fourth onward…

Q: Prove that {a"b"} is CFL but {a"b"c"} is not for n>=0.

A: Given , {a^nb^nc^n | n>=0}

Q: This sum of minterms F(A, B, C, D) (1,3,5, 7,9, 11, 13, 15) is equivalent to which product of…

A: