An instance is a machine instance of the NP core: a finite structure describing a Turing machine with its input and a linear order of positions. The machine accepts in bounded space when some run from an initial configuration reaches an accepting state, whatever its length: the tape is the set of positions, so the space is bounded by the instance, while the number of steps is not. An instance is a yes-instance of machine acceptance in bounded space when it is well formed and accepts in this sense, and of its deterministic variant when the machine is moreover deterministic; each problem is the decision problem of the structures isomorphic to such an instance.