nfa_step

std.seq.nfa_step · Level L3

One symbol of a nondeterministic finite automaton run on the set of current states (a 0/1 vector): every transition on the symbol, then every ε-move, through the ε-closure C. The body nfa_accepts scans.

S′ = min(1, S·T_σ·C)

Signature

nfa_step(S: f64[k], symbol: i64[], T: f64[a, k, k], C: f64[k, k]) → f64[k]

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 min(1, (S @ T[symbol]) @ C) in exact rational arithmetic, on all 40 test cases.
All 135 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

vecmat

Called by

nfa_accepts

sha256:d057567dc59986c8035d7df6d25450036d7fe3973be78e466300b0827b6da0dc

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.nfa_step · Ω:nfa_step
Pins: sha256:a133f8996d4470db6fa08e5cb20b7116b68496df5c335ec7923609cb168f95d6this graph and the 1 it reaches through calls
Evidence: sha256:d56f454d71a9ea3d06d6c7a05a8abc6bb94518d0b5c28a96be942b4c6b889c4fthe 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.