Complexity theory results

Type: KNOWLEDGE

Verification: sources_verified - Evidence: verified_report

Quality: public

## Key Findings - Title: Recent Advances in Complexity Theory (as of April 12, 2026)** - Key Developments in Complexity Theory (2024–2026)** - 1. **Breakthrough on the Complexity of Matrix Multiplication** - In January 2025, researchers Alman, Williams, and Xu improved the upper bound for matrix multiplication complexity to *O(n².³⁷¹⁵⁵²)* using a new automated framework that searches for efficient tensor decompositions via SAT solvers and algebraic geometry techniques. This marked the first...