OpenAI reports a quasilinear PCP theorem for PPAD

There are fixed positive rational ε and δ and a deterministic reduction mapping an End-of-Line instance of binary length N to a generalized circuit of length N(log N)^O(1).

Curated contributions 1

Understand the problem ↓

OpenAI reports a quasilinear PCP theorem for PPAD

  • Theoretical Computer Science

There are fixed positive rational ε and δ and a deterministic reduction mapping an End-of-Line instance of binary length N to a generalized circuit of length N(log N)^O(1). A solution to the original instance can be recovered in polynomial time from any polynomial-length rational assignment ε-satisfying all but a δ fraction of gates.

AI involvementAI-led
ImportanceMajor
Technical verificationReported
Human understandingFew

Understanding the problem

Read the background

There are fixed positive rational ε and δ and a deterministic reduction mapping an End-of-Line instance of binary length N to a generalized circuit of length N(log N)^O(1). A solution to the original instance can be recovered in polynomial time from any polynomial-length rational assignment ε-satisfying all but a δ fraction of gates.

Why it matters

If correct, resolves the quasilinear-size PCP-for-PPAD conjecture of Babichenko, Papadimitriou, and Rubinstein.

What counts as progress

Can PPAD hardness survive a fixed fraction of erroneous generalized-circuit gates with quasilinear reduction size?

Website timeline

Publication dates and editorial changes.