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Consider a database whose universe is a finite set of vertices V and whose unique relation .E is binary and encodes the edges of an undirected (resp., directed) graph G: (V, E). Each undirected edge between the nodes o and u (resp., directed edge from the node v to the node u) is encoded by the two atoms E (v, u) and E (u, v) (resp., by the single atom E (v, u)).
Consider the pairs of stucture (undirected (resp., directed) graphs) shown in Fig. 1. Suppose that the graphs are encoded in a database as explained above. For each pair, answer the following questions:
1. What is the smallest quantifier rank k for which the spoiler wins the k-move Ehrenfeucht-Fraisse game on the pair of structure?
2. Derive a Boolean first-order query from your winning strategy that is true on one structure but not on the other (you can use the equality relation between vertices).
PROBLEMS WITH APPLYING ALGORITHMS : From your experience, you would agree that children are expected to mechanically apply the algorithms for adding or subtracting numbers, regar
1. Let M be the PDA with states Q = {q0, q1, and q2}, final states F = {q1, q2} and transition function δ(q0, a, λ) = {[q0, A]} δ(q0, λ , λ) = {[q1, λ]} δ(q0, b, A) = {[q2
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The sum of areas of two squares is 468m 2 If the difference of their perimeters is 24cm, find the sides of the two squares. Ans: Let the side of the larger square be x .
Find all the local maximum and minimum values and saddle points of the function f(x, y) = x 2 - xy + y 2 + 9x - 6y + 10
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Determine the tangent line to f ( x ) = 15 - 2x 2 at x = 1. Solution : We know from algebra that to determine the equation of a line we require either two points onto the li
an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 30 years hence is 2/3.Find the p
The subsequent force that we want to consider is damping. This force may or may not be there for any specified problem. Dampers work to counteract any movement. There are some w
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