Near-Optimal Scheduling for LTL with Future Discounting

We study synthesis of optimal schedulers for the linear temporal logic (LTL) with future discounting. The logic, introduced by Almagor, Boker and Kupferman, is a quantitative variant of LTL in which an event in the far future has only discounted contribution to a truth value (that is a real number in the unit interval [0, 1]). The precise problem we study—it naturally arises e.g. in search for a scheduler that recovers from an internal error state as soon as possible— is the following: given a Kripke frame, a formula and a number in [0, 1] called a margin, find a path of the Kripke frame that is optimal with respect to the formula up to the prescribed margin (a truly optimal path may not exist). We present an algorithm for the problem: it relies on a translation to quantitative automata and their optimal value problem, a technique that is potentially useful also in other settings of optimality synthesis.