Adding an ending-to-starting edge to exactly simulate instantaneous transitions

Demonstrate that introducing an additional transition (edge) from the ending location to the starting location in each action automaton enables exact simulation of the intended instantaneous end-to-start scheduling step, and prove that the modified network of timed automata preserves the temporal-planning semantics under the paper’s mutex and invariant conditions.

Background

The authors extend the classical encoding with an intermediate edge (ie_a) to better capture instantaneous snap actions. They further hypothesize that another edge connecting ending to starting could eliminate remaining gaps in exact simulation of instantaneous transitions.

Proving that this structural augmentation preserves correctness and provides exact fidelity would close a remaining modeling gap and strengthen the encoding’s coverage of instantaneous behaviors.