Forgotten-action frontier machine

Exact statement

A forgotten-action frontier machine has a finite transition list $(q,a,X,q',\gamma)$ , an explicit initial configuration, and final-state acceptance. Each transition consumes one input symbol and replaces the leftmost stack symbol (X) by $\gamma$ ; there are no epsilon or endmarker steps. Its frontier component (S_u(q)) contains exactly the stacks reachable in control state (q) after the observed prefix (u).

StatusDefined self-containedly and used by the checked recurrence

External reviewNo documented external or specialist review of this FPRD exposition is recorded.

Context

Forgetting call, return, and local tags turns one deterministic tagged run into a finite set of possible untagged configurations after each prefix.

Definitions

A transition $(q,a,X,q',\gamma)$ maps ((q,Xv)) to $(q',\gamma v)$ while consuming (a).
$S_u(q)=\{z:(q_0,z_0)\xRightarrow{u}(q,z)\}$ .

Proof or evidence

The exact transition semantics, initial frontier, and final-state readout are implemented in the standalone Lean development.

Machine and frontier →

Verification notes

The public definition was checked against the repository specification and the executable transition-list model, including empty input and the absence of hidden endmarker work.

Limitations

The definition does not assert that every frontier has a bounded persistent representation.
It does not identify the machine with a visibly pushdown automaton after the action tags have been forgotten.

Open work

Use this fixed interface when comparing stationary frontier representations; do not conflate it with a PEG or scaffold.

Notes

This definition pins the presentation, generated frontier dynamic, and readout without identifying them with a PEG or scaffold. It does not prove CFL is contained in PEL or separated from PEL, and it opens no M34.