Is it Easier to Prove Statements that are Guaranteed to be True?

Explore the intriguing question of whether statements guaranteed to be true are easier to prove in this 26-minute IEEE conference talk by Rafael Pass from Cornell Tech and Muthuramakrishnan Venkitasubramaniam from the University of Rochester. Delve into topics such as worst-case vs. average-case hardness, the Challenger-Solver game, and the hardness of Promise-true NP-Search problems. Examine machine learning concepts, including local search and Nash Equilibrium, before tackling open problems related to restricted distributions and one-way functions. Investigate the average-case hardness of NP, interactive puzzles, and the failure of the Babai-Moran Transformation for computational soundness. Gain insights into the main theorem, its proof overview, and the concluding remarks that tie together these complex concepts in computational theory.

Intro
Worst-case vs Average-case Hardness
Challenger - Solver game G89,195
Hardness of Promise-true NP-Search
Promise-true NP-Search problems
Machine Learning: Local Search JPY'88
Nash Equilibrium
Open Problem 1
Restricted Distributions: One-way functions
Open Problem 2
Average-case Hardness of NP [K73,L86]
Main Theorem
Proof Overview
Interactive Puzzles
2-round Puzzles
Main Question
Failure of Babai-Moran Transformation for computational soundness
Main Lemma: If a OWF, BM-transformation works
Concluding the proof
Concluding Remarks