What are the theoretical limits of computation, as defined by concepts such as Turing completeness, computational complexity, and the Church-Turing thesis? Furthermore, how do these concepts inform our understanding of algorithmic efficiency and computability?

Theoretical limits of computation address questions about what can and cannot be computed within the constraints of formal systems. Concepts such as Turing completeness, computational complexity classes (e.g., P vs. NP), and the Church-Turing thesis provide frameworks for understanding the capabilities and limitations of algorithms and computers, influencing fields such as cryptography, optimization, and artificial intelligence.