max_clique

std.linalg.max_clique · Level L4

The clique number ω(G) of a finite undirected simple graph, a maximum clique as a 0/1 vector (the first in counter order), and the number of maximum cliques: every vertex subset is tested, 2ⁿ of them, in a While over clique_step. A maximal clique (one no vertex can join) need not be maximum; only the full search shows that none is larger. ω(G) ≤ χ(G), and the two can differ.

ω(G) = max{|S| : S a clique}

Signature

max_clique(A: f64[n, n]) → f64[], f64[n], f64[]

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 every subset in counter order: the first largest clique, and how many there are in exact rational arithmetic, on all 40 test cases.
All 214 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

clique_open clique_step growth_step

Called by

max_independent_set

sha256:7c3ef584a1c75d10713dd86acb2d449b2cba92c78d1a3f86deb537fb0b4b4268

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.max_clique · Ω:max_clique
Pins: sha256:ae88c92dcaec6b43dbf93addffeb574c9a2ab036550b6ba61e7e49ecbe014620this graph and the 5 it reaches through calls
Evidence: sha256:1dcf4040118b302e6e06a41d1b4af7cdabd7f84fc191656b7a2c7343371a06fethe 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.