pda_run_check

std.seq.pda_run_check · Level L3

Whether a given run, a list of transition indices, is an accepting run of a pushdown automaton on a word, as 1 or 0: every step fits its configuration (pda_step), the whole input is read, and the final state is accepting (acceptance by final state, not by empty stack); and whether every step fitted. A run is a witness of membership; failing to find one by a bounded search proves nothing, and says nothing about the automaton's determinism or its grammar.

(q₀, 0, Z) ⊢* (q, |w|, γ), q ∈ F

Signature

pda_run_check(start: f64[], stack0: f64[H], h0: f64[], Tfrom: i64[t], Tin: i64[t], Ttop: i64[t], Tto: i64[t], Tlen: i64[t], Tpush: i64[t, 2], accept: f64[Q], word: i64[L], run: i64[m]) → 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 the same steps on Python lists 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

pda_step

Called by

—

sha256:52fa7f7879937d592ae0e9d903f98c695745589ed385e55499efcd35dcf7855e

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.pda_run_check · Ω:pda_run_check
Pins: sha256:f1c72d72dbd010c3390dc2ee7906d0bb0ed80c305ba1d1653454c251b7429b9ethis graph and the 1 it reaches through calls
Evidence: sha256:cbe8e5573cf36bdcd4cc814b8d50f0ca7b26024313df8a5883cdc09998671582the 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.