Constructing an unobservable critical path network from observable slacks

Critical Path Networks are models of the Psychological Refractory Period and of some cognitive tasks, such as visual search. A Critical Path Network is a directed acyclic network in which each arc represents a process that must be completed to perform a task, The processes on a path must be executed in order on the path. Processes not on a path together are unordered, and can be executed simultaneously. Each process has a duration. The time to complete the task, the response time, is the sum of the durations of the processes on the longest path through the network. If a process X precedes a process Y, the slack from X to Y is the longest amount of time by which X can be prolonged without making Y start late. Suppose processes in a task are executed in a Critical Path Network, but the network is unknown. By observing effects on response time of selectively influencing processes, one can learn for each pair of processes whether the pair is ordered or unordered. If they are ordered, one can learn the value of the slack from one to the other. From the order information a directed acyclic network can be constructed with the Transitive Orientation Algorithm. From the slacks a duration can be determined for each process. Several directed acyclic networks may be possible and the durations are not unique. If the slack values are valid for one of the possible directed acyclic networks, they are valid for all.