Decidability of simulation and bisimulation for higher-dimensional timed automata (HDTAs)

Establish the decidability of simulation and bisimulation relations for higher-dimensional timed automata (HDTAs) by first formulating precise notions of simulation and bisimulation for HDTAs and then proving that checking these relations is decidable, in analogy with the decidability known for timed automata.

Background

The paper introduces languages for higher-dimensional timed automata (HDTAs) via timed ipomsets and interval delay words, proving undecidability of language inclusion and decidability of untimed language inclusion. In the closing Perspectives, the authors outline directions needed to enable real-time concurrent model checking for HDTAs, notably simulation and bisimulation analyses.

For classical timed automata, several notions of simulation and bisimulation are known and checking these relations is decidable. The authors explicitly conjecture that analogous notions for HDTAs should also be decidable, highlighting a concrete and central open problem at the interface of HDTA theory and verification.