Manuscript XIX-C@1 · XIX-C.tex · section · 98b067d9

Scheduled ancestry

The complete finite-register support ceiling › Scheduled ancestry · lines 793–811

XIX-C@1#eq:ancestors

At tick $k$ , let $B_{k}$ be a partition of $X$ and let

Φ_{k} = B \in B_{k} ⨂ Φ_{k, B}

be a product of block channels. For an output set $Y$ at tick $t$ , define

N_{t, t} (Y) N_{s, t} (Y) = Y, = ⋃ {B \in B_{s + 1} : B \cap N_{s + 1, t} (Y) \neq = \emptyset}, s < t .

These are conservative scheduled ancestor sets, not necessarily minimal actual supports.

Displayed formulas in this passage

XIX-C@1#eq:ancestors · line 801
$N_{t, t} (Y) N_{s, t} (Y) = Y, = ⋃ {B \in B_{s + 1} : B \cap N_{s + 1, t} (Y) \neq = \emptyset}, s < t .$
unlabeled · line 796
$Φ_{k} = B \in B_{k} ⨂ Φ_{k, B}$