Trajectory Specification is a method of specifying aircraft trajectories with tolerances such that the position at any given time in flight is constrained to a precisely defined bounding space. The bounding space is defined by tolerances relative to a reference trajectory that specifies position as a function of time. The tolerances are dynamic and are based on the aircraft navigation capabilities and the Traffic situation. Trajectory Specification can guarantee safe separation for an arbitrary period of time even in the event of an air Traffic control (ATC) system or datalink failure. It can help to achieve the high level of safety and reliability needed for ATC automation, and it can also reduce the reliance on tactical ATC backup systems during normal operation. This paper presents algorithms and software for detecting and resolving conflicts between specified trajectories in the terminal airspace serving a major airport. In a fast-time simulation of a full day of Traffic in a major terminal airspace, all conflicts were resolved in near real time, demonstrating the computational feasibility and the preliminary operational feasibility of the concept.