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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).
Discuss demanding total market demand verus gaing market share
The population of a city is observed as growing exponentially according to the function P(t) = P0 e kt , where the population doubled in the first 50 years. (a) Find k to three
Is the group of order 10 simple?
The functions {sinmx; cosmx}; m = 0,....∞ form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these
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Natureland garden center buys lawn mowers that list for $679.95 less a 30% discount. What is the dollar amount of the discount?
Arc Length for Parametric Equations L = ∫ β α √ ((dx/dt) 2 + (dy/dt) 2 ) dt Note: that we could have utilized the second formula for ds above is we had supposed inste
Simple derivatives Example Differentiate following. (5x 3 - 7 x + 1) 5 ,[ f ( x )] 5 ,[ y ( x )] 5 Solution: Here , with the first function we're being asked to
Rob purchased picnic food for $33.20 to share along with three of his friends. They plan to split the cost evenly among the four friends. How much does every person required to pay
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