Linear dynamical systems with continuous weight functions

Rajab AghamovRajab Aghamov, Christel BaierChristel Baier, Toghrul KarimovToghrul Karimov, Joël OuaknineJoël Ouaknine, Jakob PiribauerJakob Piribauer

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Rajab Aghamov, Christel Baier, Toghrul Karimov, Joël Ouaknine, Jakob Piribauer
Linear dynamical systems with continuous weight functions
In Erika Ábrahám and Manuel Mazo Jr., eds., Proceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2024, Hong Kong SAR, China, May 14-16, 2024, 22:1--22:11, 2024. ACM

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KurzfassungAbstract
In discrete-time linear dynamical systems (LDSs), a linear map is repeatedly applied to an initial vector yielding a sequence of vectors called the orbit of the system. A weight function assigning weights to the points in the orbit can be used to model quantitative aspects, such as resource consumption, of a system modelled by an LDS. This paper addresses the problems to compute the mean payoff, the total accumulated weight, and the discounted accumulated weight of the orbit under continuous weight functions and polynomial weight functions as a special case. Besides general LDSs, the special cases of stochastic LDSs and of LDSs with bounded orbits are considered. Furthermore, the problem of deciding whether an energy constraint is satisfied by the weighted orbit, i.e., whether the accumulated weight never drops below a given bound, is analysed.
Forschungsgruppe:Research Group: Algebraische und logische Grundlagen der InformatikAlgebraic and Logical Foundations of Computer Science

@inproceedings{ABKOP2024,
  author    = {Rajab Aghamov and Christel Baier and Toghrul Karimov and
               Jo{\"{e}}l Ouaknine and Jakob Piribauer},
  title     = {Linear dynamical systems with continuous weight functions},
  editor    = {Erika {\'{A}}brah{\'{a}}m and Manuel Mazo Jr.},
  booktitle = {Proceedings of the 27th {ACM} International Conference on Hybrid
               Systems: Computation and Control, {HSCC} 2024, Hong Kong {SAR,}
               China, May 14-16, 2024},
  publisher = {ACM},
  year      = {2024},
  pages     = {22:1--22:11},
  doi       = {10.1145/3641513.3650173}
}