Interval Comparisons and Lattice Operations based on the Interval Overlapping Relation

Based on the overlapping relation the paper then identifies 7 atomic independent interval operations, which form a base for the binary relation algebra (BRA) for intervals, [5]. The atomic operations can be used to compute the most commonly used interval comparisons, as those have been proposed in motion 13 [4]. Hence, this paper contributes to the rationale of motion 13. The next section introduces the necessary lattice operations which are closely related with comparisons. These also can be derived from the overlapping relation. In [6] we have shown that the general overlapping relation can be efficiently implemented in hardware. 4 bits are sufficient to encode the different states. Together with an object oriented interface allowing the direct access to the states (cases) this will presumably lead to a better performance of application programs.