augmentable

std.linalg.augmentable · Level L2

Whether the sink n − 1 is reachable from the source 0 in the residual network C − F, as 1 or 0: an augmenting path exists. The condition max_flow loops on.

[0 ⇝ n − 1 in C − F]

Signature

augmentable(F: f64[n, n], C: f64[n, n]) → f64[]

Requires: n ≥ 2

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size with n ≥ 2.
Equal to the reference BFS reaches the sink in C − F in exact rational arithmetic, on all 40 test cases.
All 40 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

residual_bfs

Called by

max_flow

sha256:93ea9085866623324e7cf9a9a9671e3e56bf9d72385fb44400366d353b215e7e

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.linalg.augmentable · Ω:augmentable
Pins: sha256:932c397a3d013471999958d67792e2ce6dad8f7804bca4ef2a9b7c2ac219e9c2this graph and the 2 it reaches through calls
Evidence: sha256:5b2de3bd4194ac32d2101124d1d695106a0e98496a67a50b0234e6d80c082407the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.