Petr Savicky

For any Boolean function $f$ let $L(f)$ be its formula size

complexity in the basis $\{\land,\oplus,1\}$. For every $n$ and

every $k\le n/2$, we describe a probabilistic distribution

on formulas in the basis $\{\land,\oplus,1\}$ in some given set of

$n$ variables and of the ...
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Scott Garrabrant, Tsvi Benson-Tilsen, Andrew Critch, Nate Soares, Jessica Taylor

We present a computable algorithm that assigns probabilities to every logical statement in a given formal language, and refines those probabilities over time. For instance, if the language is Peano arithmetic, it assigns probabilities to all arithmetical statements, including claims about the twin prime conjecture, the outputs of long-running ... more >>>