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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).
3.6 in a fraction
One-to-one function: A function is called one-to-one if not any two values of x produce the same y. Mathematically specking, this is the same as saying, f ( x 1 ) ≠ f ( x 2
encoded with the matrix -3 -7 and 4 9. what lights up a soccer stadium? ecoded message: {-3 - 7} {3 2 } {3 6} {57 127} {52 127} {77 173} {23 51)
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find a quadratic equation whose roots are q+1/2 and 2p-1 with p+q=1
1. Suppose the arrival times of phone calls in a help centre follow a Poisson process with rate 20 per hour (so the inter-arrival times are independent exponential random variables
Which number falls among 5.56 and 5.81? If you add a zero to the end of 5.6 to get 5.60, it is simpler to see that 5.56
Determine if the acceleration of an object is given by a → = i → + 2 j → + 6tk → find out the object's velocity and position functions here given that the initial velocity is v
What is the prime factorization of 84? This is the only answer choice which has only PRIME numbers. A prime number is a number along with two and only two distinct factors. In
We have to enclose a field along with a fence. We contain 500 feet of fencing material & a building is on one side of the field & thus won't require any fencing. Find out the dime
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