What does this equation mean?

Irving, Christiano, and Amodei’s 2018 “AI Safety via Debate” proposed one answer: train two copies of a model to argue opposing sides of a question in front of a human judge, under a length limit, with the judge deciding which debater was more helpful and honest [ 9 ] . The paper’s own framing draws an explicit analogy to computational complexity theory, arguing that a judge relying on a single unverified report is limited to adjudicating claims a bounded verifier can check directly, while a judge equipped with a structured, adversarial debate between two competing reporters can in principle adjudicate a substantially larger class of claims, since each debater is incentivized to expose flaws in the other’s argument that the judge alone would not have found: $\text{judge alone} \approx \mathrm{NP}, \qquad \text{judge} + \text{debate (polynomially many rounds)} \approx \mathrm{PSPACE}$. That relation is the paper’s real theoretical claim, not decoration: it is the specific argument for why debate should, in principle, extend how complex a claim a time-limited human judge can reliably oversee, and the paper reports early supporting evidence from a simplified image-classification setting where a debate-trained judge’s accuracy rose from 59.4% to 88.9% relative to a judge working from limited direct evidence alone [ 9 ] .