Transfer the precision-based PSPACE characterization to polynomial ODEs

Determine whether the algebra RCD, which characterizes FPSPACE via robust continuous ordinary differential equations and identifies space complexity with required numerical precision, can be fully transferred to the setting of polynomial ordinary differential equations so that the same FPSPACE characterization holds and precision directly captures space complexity at the polynomial ODE level.

Background

The paper introduces the algebra RCD defined by basic analytic functions together with composition and a robust ODE schema, and proves that its discrete parts capture FPSPACE. A central conceptual contribution is the identification of space complexity with the precision required to simulate numerically stable continuous-time ODEs.

While earlier PSPACE characterizations for polynomial ODEs exist, they rely on ad-hoc conditions and unbounded domains. The authors ask whether their simpler precision-based framework can be realized directly with polynomial ODEs, providing a clean link between space and precision in this restricted and well-studied class of ODEs.