refactor(MultiTapeTM): Make the deterministic machine a nondeterministic one - #821
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refactor(MultiTapeTM): Make the deterministic machine a nondeterministic one#821barni120400 wants to merge 6 commits into
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The configuration gains an `output` field holding the symbols emitted so far, `step` appends to it and `initCfg` starts it empty. The output of a run can then be read off its final configuration, so `outputString` and its lemmas are replaced by `step_output` and existing facts about `configs`, and `ComputesInTimeAndSpace` reads the output from the configuration it already mentions. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
`configs` returns the single configuration reached after `t` steps, not a sequence of configurations, so the plural name did not match the type. It also depends on `tm` only through its step function. Renamed to `runFrom`, along with its five lemmas. Pure rename, no change to any statement or proof. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Keep the design section free of storage details, list the output tape among a configuration's components, and drop the stale `BiTape` mention. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
A nondeterministic machine replaces the transition function by a transition relation. Configurations and the effect of an action move to a shared `MultiTape/Configuration.lean`; no existing statement changes meaning. A computation path is a `RelSeries` of the step relation starting at the initial configuration, so Mathlib supplies its length, the configurations it passes through, and the one it ends at. `MultiTapeTM.toNTM` embeds the deterministic machine and `toNTM_computes` shows the embedding preserves computation in bounded time and space. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
…tic one `MultiTapeTM` now extends `MultiTapeNTM`, permitting exactly the transition its transition function prescribes, with `ofTr` building one from a transition function. Everything defined for the nondeterministic machine therefore applies to it, and the separate embedding file is gone. Determinism makes those notions concrete: a step is what `step` computes (`ntmStep_iff`, replacing `TransitionRelation`), every computation is the machine's own run (`computation_toFun`), and computing is a statement about that run (`computesInTimeAndSpace_iff`). Space is now defined once, on `Computation`. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
…e space measures A `Run` is a series of steps from anywhere; a `Computation` is a run starting at the initial configuration. `visited`, `spaceByTape` and `space` are therefore defined for arbitrary runs, and the lemmas about them live with the other tape lemmas. `spaceUsed_eq_run_space` relates the deterministic measures to them from any configuration. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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Builds on #820 — only the last commit is new here.
MultiTapeTMnow extendsMultiTapeNTM, permitting exactly the transition its transition function prescribes, withofTrbuilding one from a transition function. Everything defined for the nondeterministic machine therefore applies to it directly, and the separate embedding file is gone.Determinism makes those notions concrete: a step is what
stepcomputes, every computation is the machine's own run, and computing is a statement about that run. Space is now defined once, on a computation.NB: claude was used heavily throughout.