Decidability of the two-clock case over dense time

Ascertain the decidability status of the execution-time opacity problems that remain unresolved for parametric timed automata with two clocks over dense time, in particular full execution-time opacity emptiness and synthesis for (2,0,1)-PTAs as highlighted in the summary table.

Background

The paper focuses on one-clock PTAs due to known undecidability results for three clocks and the difficulty of the two-clock case even for reachability. The summary table marks several items as open for configurations involving two clocks over dense time.

The authors explicitly point out that multiple entries remain open, with the two-clock case being a notable and challenging frontier. Establishing decidability (or proving undecidability) for these two-clock configurations would significantly advance the theory of execution-time opacity in PTAs.