We re-examine the complexity of evaluating monotone planar circuits
MPCVP, with special attention to circuits with cylindrical
embeddings. MPCVP is known to be in NC^3, and for the special
case of upward stratified circuits, it is known to be in
LogDCFL. We characterize cylindricality, which ... more >>>

In this paper, we study the circuit value problem for monotone Boolean circuits (that is, circuits without negation gates) when the circuits are embedded on a surface of bounded genus, and all inputs to the circuits lie on at most constantly many faces. We show that this problem can be ... more >>>

Williams (STOC 2025) recently proved that time-$t$ multitape Turing machines can be simulated using $O(\sqrt{t \log t})$ space using the Cook-Mertz (STOC 2024) tree evaluation procedure. As Williams notes, applying this result to fast algorithms for the circuit value problem implies an $O(\sqrt{s} \cdot \mathrm{polylog}\; s)$ space algorithm for evaluating ... more >>>