decides

std.sets.decides · Level L2

Whether a decider's answers D(x) (0 or 1, for every input x of a finite input set) decide the problem with yes-instances Y, as 1 or 0: D(x) = 1 exactly when x ∈ Y; and the first input where they differ (0 when none). A finite table settles that finite input set only; decidability of an infinite problem needs an algorithm that halts on every input.

D(x) = [x ∈ Y] ∀x

Signature

decides(D: f64[n], Y: f64[n]) → 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 every answer against Y, and the first mismatch in exact rational arithmetic, on all 40 test cases.
All 80 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

—

Called by

—

sha256:fae470b63aa67d172fb11a7c2e9ff9dd1a87b0b4cefd169609dd9e1cf42a1e67

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.sets.decides · Ω:decides
Pins: sha256:5a6eba18993906a2dc4b3b6ce6f0707c62d46b81d3ee4078f11ecb00e9347d82this graph alone
Evidence: sha256:8dce34c7da24be32e9afb70c5d7d8a19089bd46d2138631d34e370d3088f0e75the 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.