TILING and CORRIDOR, the umbrella

The two questions a tile system is asked: tiling the square whose sides are the positions of the instance (DescriptiveComplexity.Problems.Tiling.Defs, with its membership in DescriptiveComplexity.Problems.Tiling.Membership), and tiling the corridor of that width and unbounded height (DescriptiveComplexity.Problems.Tiling.Corridor, with its membership in DescriptiveComplexity.Problems.Tiling.CorridorMem).

The point of the two is what they become one exponential up: read over an exponential expansion, the same definitions ask about a 2ⁿ × 2ⁿ square and a corridor of width 2ⁿ, which are the classical second complete problems of NEXPTIME and of EXPSPACE beside a machine.