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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).
i don''t understand how
Differentiate following. f ( x ) = sin (3x 2 + x ) Solution It looks as the outside function is the sine & the inside function is 3x 2 +x. The derivative is then.
how can you tell qhich trangle is sss,asa, sas, and aas s
Spring, F s We are going to suppose that Hooke's Law will govern the force as the spring exerts on the object. This force will all the time be present suitably and is F s
Basic "computation" formulas : Next, let's take a quick look at some basic "computation" formulas that will let us to actually compute some derivatives. Formulas 1) If f
#k1=f(Tn, Xn), k2=f (Tn + H.Y,Xn + H.Y.k1) Xn+1=Xn + H(a.k1+ b.k2) Find a relation between Y,a and b so that the method is second order consistent.
Evaluate the slope of the line: Example: What is the slope of the line passing through the points (20, 85) and (30, 125)? Solution: m = 125 -85/30-20 = 4
SUMMATION NOTATION Under this section we require to do a brief review of summation notation or sigma notation. We will start out with two integers, n and m, along with n a
There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys
Infinite Limits : In this section we will see limits whose value is infinity or minus infinity. The primary thing we have to probably do here is to define just what we mean w
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