Seiller, T., Pellissier, L., & Léchine, U. (2024). Unifying lower bounds for algebraic machines, semantically [Preprint]. arXiv:1811.06787v4 [cs.CC].
This paper aims to introduce a new abstract method for proving lower bounds in computational complexity, specifically for algebraic models of computation. The authors utilize the concept of topological and measurable entropy from dynamical systems theory to achieve this.
The authors represent programs as graphings, which are generalized dynamical systems. They then leverage the concept of topological entropy to analyze the complexity of these graphings. By establishing a connection between the entropy of a graphing and the complexity of the corresponding program, they derive lower bounds for various algebraic models.
The paper presents a powerful new method for proving lower bounds in algebraic complexity theory based on topological entropy. This method provides a unifying framework for understanding existing lower bound results and enables the derivation of new, stronger lower bounds for various algebraic models of computation.
This research significantly contributes to the field of computational complexity by introducing a novel and powerful method for proving lower bounds. The use of topological entropy offers a fresh perspective on analyzing the complexity of algebraic models and opens up new avenues for future research in this area.
While the paper focuses on algebraic models of computation, future research could explore the applicability of this method to Boolean models. Additionally, investigating the potential of using topological entropy to derive even tighter lower bounds for specific problems and models presents a promising direction for future work.
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