minizinc-benchmarks | A suite of MiniZinc benchmarks

Both the original MiniZinc model and the one in the repository in the comment are ones I wrote. While my licentiate thesis and the linked repository use regular expressions to express the constraints, the original MiniZinc challenge model was written when MiniZinc only had support for DFA inputs, as this is what the regular constraint inside solvers actually use (§). The DFAs were in fact generated by taking the Gecode model and writing a small program (lost to time) that printed out the DFA for the regular expressions in the Gecode example file using the Gecode regular expression to DFA translation. A nice thing about the translation is that for a piece that has some symmetry, the DFA minimization will remove the symmetries. The instance generator linked was written this year, and uses the modern MiniZinc feature that accepts regular expressions. It was just easier to write that way.

So, in order to understand the long list of numbers, you have to view it as a DFA. The list represent a matrix, where the indexes are the states and the next input, and the values are the next state to go to. The other arguments to the regular constraint indicate the number of states, the number of symbols in the alphabet, and the starting and accepting states of the DFA.

As for the 6's at the end of the matrix, these are end-of-line markers. They are there to make sure that a piece is not split apart. Consider the simple piece XXX on a 4 by 4 board with no other pieces (so X is 1, and empty is 0). With the expression 0*1110*, all placements of the piece are modeled, but so are placements like