Sound and Complete Algorithms for Checking the Dynamic Controllability of Temporal Networks with Uncertainty, Disjunction and Observation

Abstract—Temporal networks are data structures for repre-senting and reasoning about temporal constraints on activities. Many kinds of temporal networks have been defined in the literature, differing in their expressiveness. The simplest kinds of networks have polynomial algorithms for determining their consistency or controllability, but corresponding algorithms for more expressive networks (e.g., those that include observation nodes or disjunctive constraints) have so far been unavailable. However, recent work has introduced a new approach to such algorithms based on translating temporal networks into Timed Game Automata (TGAs) and then using off-the-shelf software to synthesize execution strategies—or determine that none exist. So far, that approach has only been used on Simple Temporal Networks with Uncertainty, for which polynomial algorithms already exist. This paper extends the temporal-network-to-TGA approach to accommodate observation nodes and disjunctive constraints. Insodoing the paper presents, for the first time, sound and complete algorithms for checking the dynamic controllability of these more expressive networks. The translations also highlight the theoretical relationships between various kinds of temporal networks and the TGA model. The new algorithms have im-mediate applications in the workflow models being developed to automate business processes, including in the health-care domain. I