Feasibility of synthesis via GH21 techniques in discrete time

Investigate whether existential execution-time opacity synthesis for parametric timed automata with one parametric clock and one parameter over discrete time can be achieved using the discrete-time reachability techniques of Gomes and Hunter (2021), which were used to obtain EXPSPACE decidability for the associated emptiness problem.

Background

In the discrete-time setting, the paper shows that existential execution-time opacity emptiness for (1,,1)-PTAs is decidable in EXPSPACE by reducing to reachability emptiness in (2,,1)-PTAs, building on Gomes and Hunter (2021).

However, the corresponding synthesis problem—computing all parameter valuations ensuring existential execution-time opacity—remains unresolved. The authors explicitly state uncertainty about whether the GH21 framework can be adapted to achieve synthesis, marking a concrete direction for future investigation.