Dynamic Controllability of Parameterized CSTNUs

A Conditional Simple Temporal Network with Uncertainty (CSTNU) models temporal constraint satisfaction problems in which the environment sets uncontrollable timepoints and conditions. The executor observes and reacts to such uncontrollable assignments as time advances with the CSTNU execution. However, there exist scenarios in which the occurrence of some future timepoints must be fixed as soon as the execution starts. We call these timepoints \textit{parameters}. For a correct execution, parameters must assume values that guarantee the possibility of satisfying all temporal constraints, whatever the environment decides the execution time for uncontrollable timepoints and the truth value of conditions, i.e., dynamic controllability (DC). Here, we formalize the extension of the CSTNU with parameters. Furthermore, we define a set of rules to check the DC of such extended CSTNU. These rules additionally solve the problem inverse to checking DC: computing restrictions on parameter values that yield DC guarantees. The proposed rules can be composed into a sound and complete procedure.