feat(MultiTapeTM): Nondeterministic multi-tape Turing machines - #802
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A nondeterministic multi-tape Turing machine is a `MultiTapeTM` whose transition function is replaced by a transition relation. Configurations, transition outputs and the effect of a single step move to a shared `MultiTape/Basic.lean`; no existing statement changes meaning. The semantics is a labelled transition system on configurations, a step labelled by the symbol it emits. A `Computation` is a chain of such transitions, with time, output and space read off it. `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>
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This adds nondeterministic multi-tape Turing machines next to the deterministic ones from #384. The transition function is replaced by a transition relation ([Papadimitriou94] 2.7); nothing else about the model changes, so configurations and the effect of a single step move to a shared
MultiTape/Basic.lean. No existing statement changes meaning.The semantics is a labelled transition system on configurations, labelled by the emitted symbol. A computation is a chain of such transitions, in the style of
SimpleGraph.Walk, recording the trajectory that space depends on and the labels that the output depends on.MultiTapeTM.toNTMembeds the deterministic machine and preserves computation in bounded time and space.