Simulation of Turing machines with analytic discrete ODEs: Polynomial-time and space over the reals characterised with discrete ordinary differential equations

Manon Blanc, Olivier Bournez

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def discrete_derivative₁ (f : ℤ → ℤ) : ℤ → ℤ

Equations

• discrete_derivative₁ f x = f (x + 1) - f x

def discrete_derivative₂ {α : Type u_1} [AddGroup α] (f : ℤ → α) : ℤ → α

Equations

• discrete_derivative₂ f x = f (x + 1) - f x