Use Rice's Theorem to prove that it is undecidable whether, for any positive integer constant k, a TM accepts exactly k strings.

Q: Let a be an integer such that a = 4 mod 12. Use the definition of mod to prove that a² = 4 mod 12-

A: Solution-:                           a≡4 mod 12a2=(4)2 mod 12     =16 mod  12     =4   mod   12

Q: Using induction on i, prove that (w) = (w) for any string w and all i ≥ 0. Hints: feel free to use…

A: Introduction Proof through Induction A proof by induction requires justification at every step, just…

Q: Let f(n) and g(n) be asymptotically nonnegative increasing functions. Prove: (f(n) + g(n))/2 =…

A: Asymmetrically non-negative, i.e. f (n) is not negative whenever n is large enough. Positive action…

Q: 'roof: given that f(0) exists, we must show that limx-o f(x)-f(0), or equivalently nat lim…

A: Please find the answer below:

Q: Use two different ways to prove XY + Z= (X+Z)(Y+Z). a) Purely Algebraic way p) K-map

A: (X+Z).(Y+Z) =X.(Y+Z) + Z.(Y+Z) =X.Y +X.Z+ Z.Y+ Z =X.Y+Z.(X+Y+1) =X.Z + Z.(X+1)  [Y+1=1] =X.Z + Z

Q: A prime number is a natural number greater than 1 which is not a product of two smaller natural…

A:

Q: Let E={〈M〉| M is a TM and every string in L(M) has even length}. Argue that the property described…

A: I Have answered this question in step 2.

Q: e define that a function f(n) has an upper bound g(n)

A: Big O notation The function  f(n) = O(g(n)) is defined when the following two properties hold: There…

Q: Question Consider the language L = {a^ | n is a prime number}. Is this language regular or…

A: Given language is, L= {an | n is a prime number} Pumping Lemma for Regular languages states that, if…

Q: * .Determine whether the function f: Z × Z →Z is onto if f (m, n) = m + n onto one to one not one to…

A:

Q: {[ {[::]-« 0 0 a (b): Let U = : a, b E R} and W: : c, d ER} be 0 0 two subspaces of M2 (R). Show…

A:

Q: Let A={+,x,a,b}. Show that (a*V ba)+ b is regular over A.

A: Answer : To show that (a*V ba)+ b is regular over A, we can construct a finite automaton that…

Q: What is the asymptotic run time of the following function? Function f(n) r = 0 for i from 0 to n for…

A: The question has been answered in step2

Q: Use the pumping lemma to prove language L, is not regular: La {1"2"3" n>0}

A: A language's irregular can be demonstrated using the pumping lemma.

Q: Prove that if n is a positive integer, then n is even if andonly if 7n + 4 is even. Prove that m2=…

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: Prove that if x, y. and z are integers and x+y + s is odd, then at least one of x, y. and z is odd.…

A:

Q: Problem 4 Prove L = {w {b,c}* | w has equal number of b's and c's, and for all prefix u of w, the…

A: L={W={b,c}*|} prove that is regular or not

Q: Find the value of x for the following sets of congruence using the Chinese remainder theorem. a. x ≡…

A: Answer

Q: et G: (0,1)" (0,1)"+l be defined as follows: (X1. ....x,) = (X, x, OX2, X OX2 O X3,X x2 ... x, X).…

A:

Q: Let f (f(n) and g(n)) be asymptotically nonnegative functions. Using the basic definition of Θ…

A: To prove that max(f(n), g(n)) = Θ(f(n) + g(n)), we need to show that there exist positive constants…

Longest Common Subsequence

The Longest Common Subsequence (LCS) is defined as the longest subsequence that is shared by all of the given sequences, assuming that the subsequence's elements do not have to be in consecutive locations in the original sequences. It is used in the areas like bioinformatic, revision control systems like SVN and Git.