conference paper published yes Ventsislav K Chonev author 36CBE2E6-F248-11E8-B48F-1D18A9856A87 Joël Ouaknine author James Worrell author KrCh department LICS: Logic in Computer Science Quantitative Graph Games: Theory and Applications project Rigorous Systems Engineering project Quantitative Reactive Modeling project The continuous evolution of a wide variety of systems, including continous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution x(t) of a system of linear differential equations dx/dt = Ax reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function f:R≥0 --&gt; R satisfying a given linear differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most 7, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order 9 (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision. IEEE2016New York, NY, USA eng 1507.03632 00038760920005210.1145/2933575.2934548 515 - 524 V. K. Chonev, J. Ouaknine, and J. Worrell, “On recurrent reachability for continuous linear dynamical systems,” in <i>LICS ’16</i>, New York, NY, USA, 2016, pp. 515–524. Chonev, Ventsislav K., et al. “On Recurrent Reachability for Continuous Linear Dynamical Systems.” <i>LICS ’16</i>, IEEE, 2016, pp. 515–24, doi:<a href="https://doi.org/10.1145/2933575.2934548">10.1145/2933575.2934548</a>. Chonev, Ventsislav K, Joël Ouaknine, and James Worrell. “On Recurrent Reachability for Continuous Linear Dynamical Systems.” In <i>LICS ’16</i>, 515–24. IEEE, 2016. <a href="https://doi.org/10.1145/2933575.2934548">https://doi.org/10.1145/2933575.2934548</a>. Chonev VK, Ouaknine J, Worrell J. On recurrent reachability for continuous linear dynamical systems. In: <i>LICS ’16</i>. IEEE; 2016:515-524. doi:<a href="https://doi.org/10.1145/2933575.2934548">10.1145/2933575.2934548</a> Chonev, V. K., Ouaknine, J., &#38; Worrell, J. (2016). On recurrent reachability for continuous linear dynamical systems. In <i>LICS ’16</i> (pp. 515–524). New York, NY, USA: IEEE. <a href="https://doi.org/10.1145/2933575.2934548">https://doi.org/10.1145/2933575.2934548</a> V.K. Chonev, J. Ouaknine, J. Worrell, in:, LICS ’16, IEEE, 2016, pp. 515–524. Chonev VK, Ouaknine J, Worrell J. 2016. On recurrent reachability for continuous linear dynamical systems. LICS ’16. LICS: Logic in Computer Science, 515–524. 13892018-12-11T11:51:44Z2025-09-22T07:31:08Z