sentences:  Usually the input is either a string (of bits or over an alphabet) and the elements of the logical structure represent positions of the string, or the input is a graph and the elements of the logical structure represent its vertices.The length of the input will be measured by the size of the respective structure.Whatever the structure is, we can assume that there are relations that can be tested, for example "formula_1 is true iff there is an edge from to " (in case of the structure being a graph), or "formula_2 is true iff the th letter of the string is 1."