#Theory
3 posts in tag “Theory”.
Kolmogorov Complexity and Algorithmic Information Theory: The Deepest Measure of Information
2025-07-30Dive into algorithmic information theory: Kolmogorov complexity as the ultimate measure of information content, its relationship to randomness (Martin-Löf tests), the incompressibility method for proving lower bounds, and the philosophical implications for science and mathematics.
The PCP Theorem: Why Some Problems Are Hard Even to Approximate
2025-03-30Unpack one of theoretical computer science's crown jewels: the PCP theorem, which shows that for many NP-hard problems, even finding an approximate solution is intractable — and how probabilistically checkable proofs revolutionized our understanding of hardness.
The FLP Impossibility Result: Why Distributed Consensus Is Fundamentally Hard
2025-01-15Explore the landmark Fischer-Lynch-Paterson result that proved no deterministic algorithm can achieve consensus in an asynchronous system with even one faulty process — and how the field evolved around this impossibility.