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        Mortality and Edge-to-Edge Reachability are Decidable on Surfaces

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        3501710.3519529.pdf (PDF, 732Kb)
        Author
        de Oliveira Oliveira, Mateus
        Tveretina, Olga
        Attention
        2299/25777
        Abstract
        The mortality problem for a given dynamical system S consists of determining whether every trajectory of S eventually halts. In this work, we show that this problem is decidable for the class of piecewise constant derivative systems on two-dimensional manifolds, also called surfaces (). Two closely related open problems are point-to-point and edge-to-edge reachability for . Building on our technique to establish decidability of mortality for , we show that the edge-to-edge reachability problem for these systems is also decidable. In this way we solve the edge-to-edge reachability case of an open problem due to Asarin, Mysore, Pnueli and Schneider [4]. This implies that the interval-to-interval version of the classical open problem of reachability for regular piecewise affine maps (PAMs) is also decidable. In other words, point-to-point reachability for regular PAMs can be effectively approximated with arbitrarily precision.
        Publication date
        2022-05-04
        Published in
        HSCC 2022 - Proceedings of the 25th ACM International Conference on Hybrid Systems
        Published version
        https://doi.org/10.1145/3501710.3519529
        Other links
        http://hdl.handle.net/2299/25777
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