feat(MultiTapeTM): add input and work tape rewinding - #873
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SamuelSchlesinger wants to merge 2 commits into
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feat(MultiTapeTM): add input and work tape rewinding#873SamuelSchlesinger wants to merge 2 commits into
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SamuelSchlesinger
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chenson2018 and
fmontesi
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September 5, 2026 21:30
This was referenced Sep 5, 2026
crei
requested changes
Sep 6, 2026
| contributes one visited cell to space. Arbitrary data on unused tapes is preserved. | ||
| - `OutputToWorkTape` redirects output to one fresh tape, including the symbol on a halting step. | ||
| - `InputFromWorkTape` simulates the native input on a work tape, preserving boundary clamping. | ||
| - `Rewind` shares one controller between native-input and work-tape rewinding. Work-tape rewind |
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I think this explanation makes uses too many terms that only become clear once you read the files.
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| One controller rewinds either the native input head or a selected work-tape head. It first moves | ||
| left, scans left through nonblank cells, then moves right and halts. The initial left move handles | ||
| a head starting on the right blank boundary, including when the contents are empty. |
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| One controller rewinds either the native input head or a selected work-tape head. It first moves | |
| left, scans left through nonblank cells, then moves right and halts. The initial left move handles | |
| a head starting on the right blank boundary, including when the contents are empty. | |
| This file defines a Turing machine that can rewind one tape in the sense of resetting the tape head | |
| to the start of the tape contents: | |
| If the tape contents are contiguous starting from the initial head position to the right and the | |
| head is positioned one cell right of the contents, then this machine will move the head to the | |
| leftmost non-blank cell. | |
| It first moves one cell left, scans left through non-blank cells, then moves right and halts. | |
| This proceduce also works when the tape is empty. |
| are allowed. Only the input head and control state change. -/ | ||
| lemma runFrom_input (cfg : Cfg k Symbol State input) : | ||
| (rewind .input).runFrom (inputCfg cfg (some .start) cfg.inputPos) | ||
| (cfg.inputPos.val - 1 + 2) = inputCfg cfg none 1 := by |
| /-! | ||
| # Halting with the input head rewound | ||
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| `rewindInput` follows an arbitrary machine with the native-input rewind controller. It preserves |
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| `rewindInput` follows an arbitrary machine with the native-input rewind controller. It preserves | |
| `rewindInput` establishes "rewound input normal form" for a Turing machine: It preserves |
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| (u : ℕ) (hhalt : (tm.runFrom cfg u).state = none) | ||
| (hactive : ∀ m < u, (tm.runFrom cfg m).state ≠ none) : |
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I saw this multiple times now (the step where the machine halts) - maybe we should create a definition for that?
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Add a shared controller for rewinding native input and contiguous work-tape contents. Use it to transform any machine into one that halts with its input head at the initial position, preserving output and work tapes.
Part 4/6 of the TM composition stack. Depends on #872. Next: #874.
Validation: strict build, import checks, full tests, and linters.
This PR was composed with Astra via Codex.