In recent years , both Williams’ original Z-buffer shadow mapping algorithm [Williams 1978] and Crow’s shadow volumes [Crow 1977] have seen many variations, additions and enhancements, greatly increasing the visual quality and efficiency of renderings using these techniques. Additionally, the fast evolution of commodity graphics hardware allows for a nearly complete mapping of these algorithms ...

I discuss recent progress in developing and exploiting connections between SAT algorithms and circuit lower bounds. The centrepiece of the article is Williams’ proof that NEXP 6⊆ ACC, which proceeds via a new algorithm for ACC-SAT beating brute-force search. His result exploits a formal connection from non-trivial SAT algorithms to circuit lower bounds. I also discuss various connections in the...