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Lax489179.TimeProperties

Monotonicity of running-time bounds

concepts/Lax489179/TimeProperties.lean · lax-489179

proven

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    Concept map

    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

    This concept declares 5 statements. Each proof establishes one of them relative to its assumptions.

    1st statement sat_exponent_mono proven

    2nd statement sat_randomized proven

    3rd statement sat_width_mono proven

    4th statement word_exponent_mono proven

    5th statement word_randomized proven

    Lemma

    Increasing a time exponent preserves solvability. A solver for width at most kk also solves every smaller SAT width. A deterministic solver is an admissible randomized solver with the same time bound.

    Lean source view on GitHub

    1import Lax489179.SATTime
    2import Lax489179.WordTime
    3
    4/-!
    5---
    6title: Monotonicity of running-time bounds
    7type: lemma
    8---
    9Increasing a time exponent preserves solvability. A solver for width
    10at most kk also solves every smaller SAT width. A deterministic solver
    11is an admissible randomized solver with the same time bound.
    12-/
    13
    14namespace Lax489179.TimeProperties
    15
    16open Algorithms
    17
    18axiom sat_exponent_mono (mode : Mode) (k : ℕ) (a b : ℝ) (hab : a ≤ b)
    19 (h : SATTime.Solvable mode k a) : SATTime.Solvable mode k b
    20
    21axiom sat_width_mono (mode : Mode) (k l : ℕ) (a : ℝ) (hkl : k ≤ l)
    22 (h : SATTime.Solvable mode l a) : SATTime.Solvable mode k a
    23
    24axiom word_exponent_mono (mode : Mode) (P : WordTime.Problem) (a b : ℝ) (hab : a ≤ b)
    25 (h : WordTime.Solvable mode P a) : WordTime.Solvable mode P b
    26
    27axiom sat_randomized (k : ℕ) (a : ℝ) (h : SATTime.Solvable .deterministic k a) :
    28 SATTime.Solvable .randomized k a
    29
    30axiom word_randomized (P : WordTime.Problem) (a : ℝ)
    31 (h : WordTime.Solvable .deterministic P a) : WordTime.Solvable .randomized P a
    32
    33end Lax489179.TimeProperties
    34
    Show ProofShow ProofShow ProofShow ProofShow Proof

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