Approximating Optimal Bounds in Prompt-LTL Realizability in Doubly-exponential Time

In this short note, we consider the optimization variant of the realizability problem for specifications in Prompt Linear Temporal Logic (Prompt-LTL), which extends Linear Temporal Logic (LTL) by the prompt eventually operator whose scope is bounded by a parametric bound. In the realizability optimization problem, one is interested in computing the optimal bound that allows to realize a given specification. It is known that this problem is solvable in triply-exponential time, but not whether it can be done in doubly-exponential time, i.e., whether it is just as hard as solving LTL realizability. We take a step towards resolving this problem by showing that the optimum can be approximated within a factor of 2 in doubly-exponential time.