WORK IN PROGRESS...

• Introduction

• Preliminaries

  • Turing machines
  • Complexity measures

• Search problems

  • Decision vs. Search
  • The complexity classes FP, FNP and TFNP
  • The TFNP hierarchy
  • White-box TFNP

• Black-box TFNP

  • Oracles and decision trees
  • Proof complexity characterization
  • An in-depth example: FP^dt = TreeRes (?)

• Parity in black-box TFNP

  • Parity decision trees and FP^pdt
  • Linear resolution over F2
  • Equivalence between PDT and Res*(+)
  • Nullstallensatz over F2
  • NS-F2 simulates Res*(+)

• Conclusions