Near-Optimal Scheduling for LTL with Future Discounting

  • Shota Nakagawa
  • Ichiro HasuoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9533)


We study the search problem for 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 works even in the extended setting with propositional quality operators, a setting where (threshold) model-checking is known to be undecidable.


Event Horizon Linear Temporal Logic Atomic Proposition Kripke Structure Tree Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Thanks are due to Shaull Almagor, Shuichi Hirahara, and the anonymous referees, for useful discussions and comments. The authors are supported by Grants-in-Aid No. 24680001, 15KT0012 and 15K11984, JSPS.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of TokyoTokyoJapan

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