are_isomorphic

std.linalg.are_isomorphic · Level L3

Whether two finite undirected simple graphs on n vertices are isomorphic, as 1 or 0, and the first isomorphism in the search order, as the image of each vertex: a bijection f with {u, v} an edge of A exactly when {f(u), f(v)} is an edge of B. Preserving edges alone is not enough; non-edges must map to non-edges too. By backtracking, a While over iso_step.

∃ bijection f : A(u, v) = B(f(u), f(v))

Signature

are_isomorphic(A: f64[n, n], B: f64[n, n]) → 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 158 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: 61%
largest error, in units in the last place: 0

Identity

Calls

iso_running iso_step

Called by

—

sha256:5fe6f8e26e24aa400aad890b7aed526a47157b0faf3ca446192c2868802c8d1c

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.are_isomorphic · Ω:are_isomorphic
Pins: sha256:a8994b74e92a3d7b6dab9c5365ae7f27d37c527ccdf32cf1c70e4a52e92086f9this graph and the 2 it reaches through calls
Evidence: sha256:e5d1a00d6fe3395d550a0b6b6e71ca23c68bc865f1a1c43ae6ed51cb4bce53bethe 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.