Revisiting Classical Dynamic Controllability: A Tighter Complexity Analysis

Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are uncontrollable (determined by nature), as is often the case for actions in planning. It is essential to verify that such networks are dynamically controllable (DC) - executable regardless of the outcomes of uncontrollable durations - and to convert them to an executable form. We use insights from incremental DC verification algorithms to re-analyze the original, classical, verification algorithm. This algorithm is the entry level algorithm for DC verification, based on a less complex and more intuitive theory than subsequent algorithms. We show that with a small modification the algorithm is transformed from pseudo-polynomial to O(n(4)) which makes it still useful. We also discuss a change reducing the amount of work performed by the algorithm.