k_colorable

std.linalg.k_colorable · Level L3

Whether a finite undirected simple graph has a proper colouring with k colours, as 1 or 0, and the first one in the search order (colours 1 … k), by backtracking: a While over color_step. A failure is a complete search, and so a proof that χ(G) > k.

[∃ proper colouring with k colours]

Signature

k_colorable(A: f64[n, n], k: f64[]) → f64[], f64[n]

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.
Equal to the reference the same backtracking search on Python lists in exact rational arithmetic, on all 40 test cases.
All 126 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

color_running color_step

Called by

chromatic_step

sha256:c3ff5ec784a2ff10d0ea24f3135d47b8e4ff112a1c079a1055798c30aa1f3173

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.k_colorable · Ω:k_colorable
Pins: sha256:9416db00d306e2255e2526874325aa998d0b8d1b91d2b09eb06921679ac0625ethis graph and the 2 it reaches through calls
Evidence: sha256:abe6046b6261612ff05e9a8475ee81d179e2c8a0ba23b3561929ffcfeb6dea8dthe 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.