## [Part7] Table Constraint

##### Question 1: Element3D

Consider a 3D Element constraint $$T[W][X][Y]=Z$$ where $$T$$ is a 3D array of integers of dimensions $$4 \times 5 \times 10$$. Assuming $$D(W)=\{0..3\}, D(X)=\{0..4\}, D(Y)=\{0..9\}, D(Z)=\{100..200\}$$, what are the dimensions (number of rows, number of columns) of the table for a Table constraint that encodes this 3D Element constraint? Write your answer in the format "nRows,nColumns", without the quotes, for instance 12,3 .

##### Question 2: Eternity II (number of tuples)

For the Eternity II edge-matching problem, assuming a 10x10 board and a set of 100 pieces that are all different and have no rotation symmetries, how many tuples does the table of each Table constraint posted in the model have?

##### Question 3: Eternity II (number of constraints)

For the Eternity II edge-matching problem, assuming a 10x10 board and a set of 100 pieces that are all different and have no rotation symmetries, how many Table constraints are posted in the model?

##### Question 4: Eternity II (table arity)

For the Eternity II edge-matching problem, assuming a 10x10 board and a set of 100 pieces that are all different and have no rotation symmetries, what is the arity (number of variables in the scope) of each Table constraint posted in the model?

##### Question 5: Regular Constraint

A Regular constraint has the form Regular:math:([x_1,...,x_n],A) where $$A$$ is a finite-state automaton:

• $$\Sigma$$ is the finite input alphabet;
• $$Q$$ is the finite set of states;
• $$\delta$$ is the transition function: $$\delta : Q \times \Sigma \rightarrow Q$$;
• $$F$$ is the set of accepting states and a subset of $$Q$$.
• $$q_0$$ is the initial state and is an element of $$Q$$;

Select all the true statements:

##### Question 6: STR2 Filtering Algorithm

In the STR2 filtering algorithm for a Table constraint, how many StateInt are necessary to maintain in a stateful way (on backtrack) the set of valid tuples?

##### Question 7: Table Constraint

Select all the true statements: