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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).
Two tangents TP and TQ are drawn to a circle with center O from an external point T.prove that angle PTQ=angle 2 OPQ
1. Construct a grammar G such that L(G) = L(M) where M is the PDA in the previous question. Then show that the word aaaabb is generated by G. 2. Prove, using the Pumping Lemma f
A 125-foot tower is located on the side of a mountain that is inclined at 32° to the horizontal. A guy wire is to be fitted to the top of the tower and anchored at a point 55 feet
The 5% sales tax on a basket was $0.70. What was the price of the basket? Use a proportion to solve the problem; part/whole = %/100. The whole is the price of the basket (wh
if prices are calculatead with a 35% markup based on cost,what is the percent that those prices should be marked down to get back to their original cost?Choose any convenient cost
The area of a square is given by the formula width time's height. But since the square has all the sides equal, the height is of the same measure as its width. Hence its formula is
Classify models based on the degree of their abstraction, and provide some examples of such models.
Suppose you start saving today for a $55,000 down payment that you plan to make on a house in 7 years, assume that you make no deposits into the account after the initial deposit,
integrate ln(1+2^t)
a boy is six months old his sister was given birth to three month after him. if their cousin is 0.33years old, arrange their ages in ascending order
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