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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).
Initial Conditions and Boundary Conditions In many problems on integration, an initial condition (y = y 0 when x = 0) or a boundary condition (y = y
Graph f ( x ) = - x 2 + 2x + 3 . Solution It is a parabola in the general form. f ( x ) = ax 2 + bx + c In this form, the x-coor
If a^n+1 + b^n+1/a^n + b^n is the arithmetic mean of a and b then find n. Answer:Arithmatic mean of a,b is =(a+b)/2 from the problem (a+b)/2=(a^n+1 +b ^n+1)/(a^n+b^n) then (a+
A circular disc of 6 cm radius is divided into three sectors with central angles 1200, 1500,900. What part of the circle is the sector with central angles 1200. Also give the ratio
construction of tangent when center not known
What is the ratio of the cone''s volume to the cylinder''s volume
Natureland garden center buys lawn mowers that list for $679.95 less a 30% discount. What is the dollar amount of the discount?
Correlation and Regression Correlation CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of
base also called what
Test of hypothesis about the difference among two means The t test can be utilized under two assumptions when testing hypothesis about the difference among the two means; that
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