| import Mathlib | |
| namespace OAI | |
| namespace Superstring | |
| abbrev Symbol := List Bool | |
| abbrev Word := List Symbol | |
| abbrev Instance := List Word | |
| /-- Prefix markers encode the list spine, including its final boundary. -/ | |
| def encodeList {α : Type} (enc : α → List Bool) : List α → List Bool | |
| | [] => [true] | |
| | a :: as => false :: (enc a ++ encodeList enc as) | |
| def encodeSymbol : Symbol → List Bool := encodeList (fun b => [b]) | |
| def encodeWord : Word → List Bool := encodeList encodeSymbol | |
| def encodeInstance : Instance → List Bool := encodeList encodeWord | |
| /-- Ordinary contiguous substring containment, including the empty word. -/ | |
| def IsCommonSuperstring (S : Instance) (T : Word) : Prop := | |
| ∀ s ∈ S, s <:+: T | |
| /-- The optimum in symbols, not in bits. -/ | |
| noncomputable def opt (S : Instance) : ℕ := | |
| sInf {n : ℕ | ∃ T : Word, IsCommonSuperstring S T ∧ T.length = n} | |
| /-- A deterministic finite-stack-machine implementation, with a polynomial bound | |
| on bit-level running time in the explicitly encoded input length. -/ | |
| def HasPolynomialImplementation (f : Instance → Word) : Prop := | |
| ∃ M : Turing.TM2ComputableInPolyTime encodeInstance encodeWord f, | |
| ∀ k : M.tm.K, Finite (M.tm.Γ k) | |
| end Superstring | |
| end OAI | |