cyk_step

std.seq.cyk_step · Level L3

One closure step of the CYK recognizer for a grammar in Chomsky normal form: X[A, i, j] = 1 when A derives the part w[i:j] of the word; for every rule A → B C (listed as RB, RC with the one-hot heads OHt) and every split point, a derivation of w[i:k] is added. The body cyk scans.

X_A ← X_A ∨ ⋁_{A → BC} X_B·X_C

Signature

cyk_step(X: f64[k, n, n], t: f64[], RB: i64[q], RC: i64[q], OHt: f64[k, q]) → f64[k, n, 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 for every rule and split point, by loops in exact rational arithmetic, on all 40 test cases.
All 3,327 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

cyk

sha256:a82e3fb4c944a539993c47668697bde9c98cca6df731ad7b97ec678177269746

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

Control handle

Symbol: Ω:std.seq.cyk_step · Ω:cyk_step
Pins: sha256:4271a9a1c4aad365dbd65b35e5466c7164073664d0a6b845a3ccdd84f72bb091this graph alone
Evidence: sha256:9e1f3cb8d6c6b02ffecef2151a43ee6b7944be5ff7d8204c5afb8ee9aa4ddfe7the 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.