Lax Lean Archive

Monotonicity of running-time bounds

Lax489179.TimeProperties · concepts/Lax489179/TimeProperties.lean · lax-489179

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Natural Language Statement

    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.

    Concept map
    8 concepts
    100%
    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.

    1 sat_exponent_mono proven

    2 sat_randomized proven

    3 sat_width_mono proven

    4 word_exponent_mono proven

    5 word_randomized proven

    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
    Builds on
    Used by

    none

    From Mathlib

    none

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above.

    Loading discussion…