walk_check

std.linalg.walk_check · Level L3

Whether a given sequence of vertices w₀ … w_k of a finite undirected simple graph is a walk, as 1 or 0: every two consecutive vertices are adjacent, so vertices and edges may repeat; whether it is a simple path, a walk with no vertex twice; and its length k, the number of edges. A single vertex is a simple path of length 0. Whether some path joins two vertices is reachability's question, not this one.

walk ⇔ A[wᵢ, wᵢ₊₁] = 1 for every i < k; simple ⇔ walk and the wᵢ distinct

Signature

walk_check(A: f64[n, n], w: i64[L]) → f64[], f64[], 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 each consecutive pair looked up in A, then the vertices counted as a set in exact rational arithmetic, on all 40 test cases.
All 120 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%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:6afeef15fd1d48c907f2729b324f17fefe0786b5844ffb1e50ebd267fb430d11

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.walk_check · Ω:walk_check
Pins: sha256:a2151a59bcd00030695e63800187950dfc21ecd6dbe4bc0e90bbe4bfda3ed790this graph alone
Evidence: sha256:4c57945e344b609e1d2aec00e9493aca50cec75b62ce706b0ad4dfdaaf55e733the 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.