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doc(LogSpace): point the BPL ⊆ P remarks at BPL_subset_P #1950

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SamuelSchlesinger merged 1 commit into from
Oct 31, 2026
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doc(LogSpace): point the BPL ⊆ P remarks at BPL_subset_P #1950

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5 changes: 3 additions & 2 deletions Complexity/Computability/Complexity/Classes/LogSpace/Randomized/BPP.lean
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Expand Up @@ -31,8 +31,9 @@ programs (`Cslib.Complexity.mem_PromiseRP_iff_exists_isPPTOn`,
(`Cslib.Complexity.BPP_subset_IP`, `Cslib.Complexity.IP_subset_PSPACE`) this gives
`BPL ⊆ PSPACE`.

The stronger inclusion `BPL ⊆ P`, by exact evaluation of the configuration matrix, is not
proved here.
The stronger inclusion `BPL ⊆ P`, by exact evaluation of the configuration matrix, is
`Cslib.Complexity.BPL_subset_P` in
`Complexity.Computability.Complexity.Classes.LogSpace.Randomized.PolyTime`.

## Main results

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5 changes: 3 additions & 2 deletions Complexity/Computability/Complexity/Classes/LogSpace/Randomized/ConfigurationMatrix.lean
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Expand Up @@ -43,8 +43,9 @@ machine on its configurations [Gill][Gill1977]. Borodin, Cook and Pippenger comp
and inverse in parallel [Borodin, Cook and Pippenger][BorodinCookPippenger1983], which gives
`BPSPACE(S) ⊆ DSPACE(S²)` [Hoza, Section 4.3][Hoza2022]; the inverse of `1 - W` as the sum
`W⁰ + W¹ + …` of transition-matrix powers is the picture of [Hoza, Section 3.2][Hoza2022].
Exact evaluation of the polynomial-size matrix also gives `BPL ⊆ P`. None of these algorithms is
formalized here.
Exact evaluation of the polynomial-size matrix also gives `BPL ⊆ P`. The parallel algorithms are
not formalized; a sequential exact evaluation, which gives `Cslib.Complexity.BPL_subset_P`, is in
`Complexity.Computability.Complexity.Classes.LogSpace.Randomized.PolyTime`.

The matrices are indexed by an arbitrary closed set of views rather than a set of
configurations of bounded size, and have no time layers: the model of `Cslib.Complexity.BPL`
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