dfa_step
std.seq.dfa_step · Level L3One transition of a deterministic finite automaton: state ← δ(state, symbol), read from the transition table δ. The body dfa_run scans.
q′ = δ(q, σ)
Signature
dfa_step(state: i64[], symbol: i64[], delta: i64[q, a]) → i64[]
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
delta[state, symbol]in exact rational arithmetic, on all 40 test cases. - All 40 int64 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 int64 nearest the exact value)
- 100%
- bit-equal to the NumPy formula in int64
- 100%
- largest error, in units in the last place
- 0
Identity
sha256:f1c3b16ecd512e0e79078f421312b69d1fe4eb05179e2bfd4443a281a97ba130The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.seq.dfa_step · Ω:dfa_step
- Pins
sha256:4b93ce763864bf899460b8732c76cf0064952ed11e1199b905beedd124adc85bthis graph alone- Evidence
sha256:adfa6f3c865532cd8037a846502e6f698b02c38f0eb338ba42d90d8e831814a3the 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.