| # Exact derandomization of logarithmic space: $`\mathsf L=\mathsf{RL}=\mathsf{BPL}`$ | |
| The following describes the scope of the Lean formalization related to the following accompanying paper(s): | |
| - [Exact derandomization of logarithmic space: L = RL = BPL](../../preprints/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPL-September-23-2026/paper.pdf) | |
| ## Scope | |
| The formalization proves $\mathsf L=\mathsf{RL}=\mathsf{BPL}$ for binary languages in an explicit Turing-machine model with logarithmic workspace. The randomized classes use polynomial time: $\mathsf{RL}$ never accepts a no-instance and accepts a yes-instance with probability at least $1/2$, while $\mathsf{BPL}$ has acceptance probability at least $2/3$ on yes-instances and at most $1/3$ on no-instances. Thus bounded-error randomness does not enlarge deterministic logarithmic space in this model. | |
| The selected theorem asserts equality of the language classes. The paper's explicit compiler and numerical running-time bounds are not separately stated in this Comparator target. | |
| ## Comparator links | |
| | Result | Comparator statement | | |
| | --- | --- | | |
| | Exact equality of deterministic and randomized logarithmic space | [LogspaceEquality.lean](../ComparatorChallenges/LogspaceEquality.lean) | | |