Question

Analyze the space and time complexity for the linear bounded automaton that accepted the set of squares.

Answer #1

Linear Algebra
Does the set of all polynomials with a_n=1 form a
linear space? Explain?

Also write the time complexity
Solve the non-linear recurrence equation using recurrence
A(n) = 2A(n/2) + n
Solve the non-linear recurrence equation using Master’s
theorem
T (n) = 16T (n/4) + n

1) Please explain why an LL(1) parser is a linear-time,
linear-space parser.
2) Please explain why an LR(1) parser is a linear-time,
linear-space parser.

In all algorithms, always prove why they work. ALWAYS, analyze
the complexity of your algorithms. In all algorithms, always try to
get the fastest possible.
A matching M = {ei} is maximal if there is no other matching M'
so that M ⊆ M' and M /= M' .
Give an algorithm that finds a maximal matching M in polynomial
time. The algorithm should be in pseudocode/plain English. Provide
the complexity of the algorithm as well.

Let X be a normed linear space. Let X* be its dual
space with the usual dual norm ||T|| = sup{ |T(x)| / ||x|| : x not
equal to 0}. Show that X* is always complete. Hint: If
Tn is a Cauchy sequence in X*, show that i)
Tn(x) converges for each fixed x in X, ii) the resulting
limits define a bounded linear functional T on X, and iii) the
sequences Tn converges to T in the norm of...

Which of the following is used to determine the linear equation
that best fits a set of data points? Question 8 options:
correlational analysis analysis of variance analysis of regression
method of least squares

(2) Let X be a set and < a linear order on X. Let S be a
subset of X. Show that if S has a least element, then S has a
unique least element.
(3) Give an example, where S has no least element. (Be sure to
specify what X, < and S are!)
(4) Let X be a set and < a linear order on X. Let S be a
subset of X which is bounded below. Show...

Let (X, d) be a metric space, and let U denote the set of all
uniformly continuous functions from X into R. (a) If f,g ∈ U and we
define (f + g) : X → R by (f + g)(x) = f(x) + g(x) for all x in X,
show that f+g∈U. In words,U is a vector space over R. (b)If f,g∈U
and we define (fg) : X → R by (fg)(x) = f(x)g(x) for all x in X,...

In class, we have studied the linear time algorithm for
selection. In that algorithm, we have used groups of size 5.
Suppose we are using groups of size 13.
• derive the corresponding recurrence formula.
• What is the corresponding time complexity of the
algorithm?
I found the reccurance relation to be
T(n)=O(n)+T(n/13)+T(19n/26), but I am having trouble finding the
time complexity. Also I really want to learn this, so a detailed
response would be nice. I believe it is...

Show that the set of sequences that satisfy the linear
recurrence equation a_n+3 − c*(a_n+2) − b*(a_n+1) − a*(a_n) = 0 is
a linear subspace of the vector space of infinite sequences. Sorry
for the clunky notation - the underscores stand to signify a
subscript.

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