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Lax434930.PolynomialTime

The complexity class P

concepts/Lax434930/PolynomialTime.lean · lax-434930

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    Definition

    A binary language belongs to P\mathrm{P} if a deterministic Turing machine decides membership in polynomial time. We reuse the definition of lax-554803 without modification: input is an ordinary binary string, output is one Boolean, and one machine and one polynomial work for all inputs.

    Lean source view on GitHub

    1import Lax554803.PolynomialTime
    2
    3/-!
    4---
    5title: The complexity class P
    6type: definition
    7---
    8A binary language belongs to P\mathrm{P} if a deterministic Turing machine
    9decides membership in polynomial time. We reuse the definition of lax-554803
    10without modification: input is an ordinary binary string, output is one
    11Boolean, and one machine and one polynomial work for all inputs.
    12-/
    13
    14namespace Lax434930.PolynomialTime
    15
    16/-- A finite binary string, as in lax-554803. -/
    17abbrev Word := Lax554803.PolynomialTime.Word
    18
    19/-- A language of finite binary strings, as in lax-554803. -/
    20abbrev Language := Lax554803.PolynomialTime.Language
    21
    22/-- Deterministic polynomial time, exactly as defined in lax-554803. -/
    23abbrev P : Set Language := Lax554803.PolynomialTime.P
    24
    25end Lax434930.PolynomialTime
    26

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