General NP-hardness of computing chaotic sequences

Ascertain whether, for chaotic maps that generate sequences exhibiting sensitivity to initial conditions (e.g., tent map, logistic map), the computational task of predicting the sequence in the complexity-theoretic sense—such as deciding threshold properties of iterates— is NP-hard for every such chaotic sequence.

Background

Beyond the tent map, the paper surveys context indicating that the computational complexity of computing chaotic sequences is underdeveloped. While some NP-complete problems exhibit chaotic behavior, a systematic complexity-theoretic classification for predictive tasks over chaotic dynamical systems is lacking.

The authors explicitly note that it is unknown whether every chaotic sequence is hard to compute in the sense of NP-hardness, highlighting a broad open direction in the theory of computation applied to dynamical systems. Clarifying this would establish whether computational hardness is an intrinsic feature of chaos across standard models.