is_vertex_cover

std.linalg.is_vertex_cover · Level L1

Whether a set of vertices C (a 0/1 vector) covers every edge of a finite undirected simple graph, as 1 or 0: an edge with neither end in C is a counterexample. The empty set covers a graph with no edges, and a superset of a cover is a cover.

[no edge {u, v} with u, v ∉ C]

Signature

is_vertex_cover(A: f64[n, n], C: 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 edge has an end in C 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

dot vecmat

Called by

—

sha256:cae0233548c39a621ca9c9ae55554d8f012669e6445da071a6ba3ba8cc447203

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.is_vertex_cover · Ω:is_vertex_cover
Pins: sha256:51619587de5a04fa4a7f784d2c9d994a7fbef5675b5763321876a97ef74f9ecdthis graph and the 2 it reaches through calls
Evidence: sha256:064a9b6a114eda0cfac9819ddf7275ff28d052f54a41beedfd47894164dfa493the 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.