Основні поняття
Decidability and complexity of robust variants of linear recurrence sequence problems.
Анотація
The article explores the robustness of linear recurrence sequences in a neighborhood of initial configurations. It delves into the Skolem problem, positivity problem, and ultimate positivity problem, analyzing their decidability and complexity. The study focuses on variants between initialized and un-initialized states, providing insights into difficult mathematical problems. The authors introduce new concepts like robust Skolem, robust positivity, and robust ultimate positivity to address challenges in real systems with imprecise initial configurations. By examining sets of initial configurations where positivity holds, the article offers geometric interpretations and novel approaches to tackle these complex problems.
Статистика
Deciding ∃-robust (non)-uniform ultimate positivity can be done in PSPACE.
Robust non-uniform ultimate positivity is decidable in PSPACE for open algebraic balls.
The Diophantine approximation type of most transcendental numbers are unknown.
Lagrange constant of a real number x is defined as L∞(x).