diff --git a/ComplexityResults/Entries.lean b/ComplexityResults/Entries.lean index 821ead1aae..5f40e5cd5c 100644 --- a/ComplexityResults/Entries.lean +++ b/ComplexityResults/Entries.lean @@ -9,6 +9,7 @@ import ComplexityResults.Registry import Complexity.Computability.Complexity.Classes.LogSpace.FirstOrder import Complexity.Computability.Complexity.Classes.LogSpace.PolyTime import Complexity.Computability.Complexity.Classes.SharpP.Lowness +import Complexity.Computability.Complexity.Classes.TimeSpace.Williams import Complexity.Computability.Complexity.FineGrained.OrthogonalVectors import Complexity.Computability.Complexity.FineGrained.PPZ import Complexity.Computability.Complexity.FineGrained.Schoening @@ -145,3 +146,17 @@ register_result "native-sparsification" where encCNF and polynomial encoded-length overhead; no new sharp sparsification \ constant." +register_result "williams-square-root-space" where + title := "Williams's square-root-space simulation of deterministic time" + topic := "space complexity" + sources := [ + { paper := Williams2025, theorem := "Theorem 1.1", + locator := "arXiv:2502.17779v1, Section 3" } + ] + theorems := [ + Cslib.Complexity.DTIME_subset_DSPACE_sqrt + ] + scope := "For every time bound t(n) >= n and arbitrary injective input encoding, \ + DTIME(t) is contained in DSPACE(Nat.sqrt(t * (Nat.log2(t) + 1))). Finite binary \ + multitape machines, read-only input and visited-work-cell space; classes absorb \ + affine constants. No time-constructibility or monotonicity hypothesis."