\begin{abstract} We present a locality--audit framework for proving circuit lower bounds for NP languages. We define an explicit NP--complete language equipped with structural invariances (``audits'') ...

Source: Darren Edwards What if one of the biggest unsolved problems in mathematics is not just about numbers or computers, but about observers like you and me? This isn’t a proposed solution to P vs ...

NP-complete problems, including optimal routing, scheduling and network design, are foundational to essential tasks across various industries. However, they actually pose challenges for conventional ...

Complexity theory remains one of the great unsolved mathematical puzzles. Kenneth Regan is trying to figure it out. Kenneth Regan paused at lunch in New York to glance at incoming texts from top ...

See the world through the lens of science. Sign up for our free, daily newsletter Today in Science. As a child of the 1990s, I couldn’t avoid the game-turned-best-seller Tetris. Launched in 1984 by ...

This repository presents a novel framework for reenvisioning the P vs NP problem through the synthesis of computational phase transitions, knowledge accumulation dynamics, and thermodynamic principles ...