Assume a 3D element constraint T[W][X][Y]=Z. T is 3D array of integers with dimensions \(4 \times 5 \times 10\). \(D(W)={0..3},D(X)={0..4},D(Y)={0..9},D(Z)=[100..200]\) We would like to model this constraint using a table constraint. What are the dimensions of the table constraint (number of rows = number of tuples, number of columns = arity of tuples/number of variables) ? Write your answer as "nRows,nColumns". For instance: 12,3

For the Eternity2 edge matching problem. Assuming a board 10x10 and a set of 100 pieces (assumed to be all different and without rotation symmetries). How many tuples will contain the table constraint ?

For the Eternity2 edge matching problem. Assuming a board 10x10 and a set of 100 pieces (they are all different and do not contain rotation symmetries). How many table constraints will be posted in the model ?

For the Eternity2 edge matching problem. Assuming a board 10x10 and a set of 100 pieces (they are all different and do not contain rotation symmetries). What will be the arity (number of variables in the scope) of any single table constraint.

A regular constraint has the form \(regular([x_1,...,x_n],automaton)\) where automaton is a finate state automaton

• \(\Sigma=\{0..k\}\) is the input alphabet (a finite, non-empty set of symbols).
• \(s_{0}\) is an initial state, an element of \(S\)
• \(\delta\) is the state-transition function: \(\delta :S\times \Sigma \rightarrow S\)
• \(F\) is the set of final states, a subset of \(S\)

We have seen that this constraint can be modeled with a table constraints.

Select all the true statements.

In the STR2 filtering algorihtm for table constraints. How many StateInt's are necessary to maintain in a reversible way (on backtrack) the set of valid tuples ?

Let us assume an implementation of the Reversible Sparse BitSet on a machine where the word length is 4 bits (instead of 64 when long are used).

Given the current state of a Reversible Sparse BitSet rsbs:

• nWords: 4
• words: 1111|1111|1111|1111
• nonZeroIdx: {0,1,2,3}
• nNonZero: 4

And the following bitsets:

• bitset1: 0001|0100|0110|0011
• bitset2: 1000|1110|0101|1010
• bitset3: 1110|0001|1001|1110

What is the resulting state of the Reversible Sparse BitSet after the following lines:

sm.saveState();
rsbs.and(bitset2);
rsbs.and(bitset3);
sm.saveState();
rsbs.and(bitset1);
sm.restoreState();

Select all the true statements