refactor(MultiTapeTM): define function complexity on inputs - #870
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SamuelSchlesinger
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chenson2018 and
fmontesi
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September 5, 2026 21:30
crei
reviewed
Sep 6, 2026
| ComputesInTimeAndSpace tm (encIn a) (encOut (f a)) t' s' | ||
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| /-- A function is computable within the input-indexed bounds by a machine with binary alphabet | ||
| and finitely many states. Input and output types may have different encodings. -/ |
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| and finitely many states. Input and output types may have different encodings. -/ | |
| and finitely many states. -/ |
I think this is redundant, input and output can be different types, so they cannot have the same encoding.
crei
reviewed
Sep 6, 2026
| ∃ (k : ℕ) (State : Type) (_ : Finite State) (tm : MultiTapeTM k Bool State), | ||
| ComputesFunInTimeAndSpace tm encIn encOut f t s | ||
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| /-- Length-based complexity is the specialization to bounds on the encoded input length. -/ |
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Can you change this docstring so that it can stand on its own? I think we should not assume that the file is read from top to bottom.
crei
reviewed
Sep 6, 2026
| obtain ⟨u, hu, v, hv, hc⟩ := h a | ||
| exact ⟨u, hu.trans (ht a), v, hv.trans (hs a), hc⟩ | ||
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| /-- Computability is monotone in its input-indexed resource bounds. -/ |
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| /-- Computability is monotone in its input-indexed resource bounds. -/ | |
| /-- Computability is monotone in the resource bounds. -/ |
crei
approved these changes
Sep 7, 2026
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Define time and space bounds on actual inputs, with explicit input and output encodings. Use binary machines with finite states for computability, and retain length-based bounds as a specialization.
Part 1/6 of the TM composition stack. Targets
main. Next: #871.Validation: strict build, import checks, full tests, and linters.
This PR was composed with Astra via Codex.