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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).
Mr. Hoper is in charge of investments for the golden horizon company. He estimates from past price fluctuations in the gold market that the probabilities of price changes on a give
Following is some more common functions that are "nice enough". Polynomials are nice enough for all x's. If f ( x) = p ( x ) /q (x ) then f(x) will be nice enough provid
Explain Linear Equations ? Set of ordered pairs of numbers A set is an undefined term and we describe it as a "well defined" collection. We use the symbol "{ }" to denote "a se
Question: Let f be a quartic polynomial (ie. a polynomial of degree 4). Suppose that f has zeros at -2; 1; 3; 4 and that f(0) = 4. Sketch a graph of f. If f(x) is
Function of a Function Suppose y is a function of z, y = f(z) and z is a function of x, z = g(x)
I figured out the volume and the width, but I have no idea how to use that information to get the height and the length!
Cylinder The below equation is the common equation of a cylinder. x 2 /a 2 + y 2 /b 2 = 1 This is known as a cylinder whose cross section is an ellipse. If a = b we
X= acost, Y= bsint find paramatric equation
which fractions is equivalent to 5/ 6 a.20/24 b.9/10 c.8/18 d.10/15
Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.
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