conference paper published yes Luca De Alfaro author Thomas A Henzinger author 40876CD8-F248-11E8-B48F-1D18A9856A870000−0002−2985−7724 Ritankar Majumdar author ICALP: Automata, Languages and Programming Discounting the future means that the value, today, of a unit payoffis 1 if the payoffo ccurs today, a if it occurs tomorrow, a 2 if it occurs the day after tomorrow, and so on, for some real-valued discount factor 0 &lt; a &lt; 1. Discounting (or inflation) is a key paradigm in economics and has been studied in Markov decision processes as well as game theory. We submit that discounting also has a natural place in systems engineering: for nonterminating systems, a potential bug in the far-away future is less troubling than a potential bug today. We therefore develop a systems theory with discounting. Our theory includes several basic elements: discounted versions of system properties that correspond to the ω-regular properties, fixpoint-based algorithms for checking discounted properties, and a quantitative notion of bisimilarity for capturing the difference between two states with respect to discounted properties. We present the theory in a general form that applies to probabilistic systems as well as multicomponent systems (games), but it readily specializes to classical transition systems. We show that discounting, besides its natural practical appeal, has also several mathematical benefits. First, the resulting theory is robust, in that small perturbations of a system can cause only small changes in the properties of the system. Second, the theory is computational, in that the values of discounted properties, as well as the discounted bisimilarity distance between states, can be computed to any desired degree of precision. Springer2003Eindhoven, The Netherlands eng 978354040493410.1007/3-540-45061-0_79 27191022 - 1037 yes De Alfaro L, Henzinger TA, Majumdar R. Discounting the future in systems theory. In: <i>Proceedings of the 30th International Colloquium on Automata, Languages and Programming</i>. Vol 2719. Springer; 2003:1022-1037. doi:<a href="https://doi.org/10.1007/3-540-45061-0_79">10.1007/3-540-45061-0_79</a> De Alfaro, Luca, et al. “Discounting the Future in Systems Theory.” <i>Proceedings of the 30th International Colloquium on Automata, Languages and Programming</i>, vol. 2719, Springer, 2003, pp. 1022–37, doi:<a href="https://doi.org/10.1007/3-540-45061-0_79">10.1007/3-540-45061-0_79</a>. L. De Alfaro, T. A. Henzinger, and R. Majumdar, “Discounting the future in systems theory,” in <i>Proceedings of the 30th International Colloquium on Automata, Languages and Programming</i>, Eindhoven, The Netherlands, 2003, vol. 2719, pp. 1022–1037. De Alfaro L, Henzinger TA, Majumdar R. 2003. Discounting the future in systems theory. Proceedings of the 30th International Colloquium on Automata, Languages and Programming. ICALP: Automata, Languages and Programming, LNCS, vol. 2719, 1022–1037. De Alfaro, Luca, Thomas A Henzinger, and Ritankar Majumdar. “Discounting the Future in Systems Theory.” In <i>Proceedings of the 30th International Colloquium on Automata, Languages and Programming</i>, 2719:1022–37. Springer, 2003. <a href="https://doi.org/10.1007/3-540-45061-0_79">https://doi.org/10.1007/3-540-45061-0_79</a>. De Alfaro, L., Henzinger, T. A., &#38; Majumdar, R. (2003). Discounting the future in systems theory. In <i>Proceedings of the 30th International Colloquium on Automata, Languages and Programming</i> (Vol. 2719, pp. 1022–1037). Eindhoven, The Netherlands: Springer. <a href="https://doi.org/10.1007/3-540-45061-0_79">https://doi.org/10.1007/3-540-45061-0_79</a> L. De Alfaro, T.A. Henzinger, R. Majumdar, in:, Proceedings of the 30th International Colloquium on Automata, Languages and Programming, Springer, 2003, pp. 1022–1037. 46282018-12-11T12:09:50Z2023-07-26T13:07:31Z