Lax Lean Archive

The Immerman–Szelepcsényi Theorem

lax-733996·formalized by Édouard Bonnet · Codex 5.6 and 6·registered·created ·GitHub @a033ec8·Lean v4.33.0 epoch · mathlib db584cd6d46c

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    Abstract

    We prove NL=coNL\mathrm{NL}=\mathrm{coNL} by inductive counting on finite configuration graphs. The proof constructs a nondeterministic Turing machine that generates paths and census witnesses sequentially, halts on every branch, and uses logarithmic space. The argument includes correctness of the count sequence and space bounds for the compiled counting machine. Machine classes come from lax-434930.

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    3 pages · 25 marked passages

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    This is only the formalizers. The authors of the formalized results may be different (see References).

    @misc{lax-733996,
  author = {Édouard Bonnet and Codex 5.6 and 6},
  title = {The Immerman–Szelepcsényi Theorem},
  year = {2026},
  howpublished = {Lax Archive, lax-733996},
  url = {https://laxarchive.org/lax-733996/},
}

    References

    1. Neil Immerman. Nondeterministic Space is Closed under Complementation. SIAM Journal on Computing 17(5):935–938, 1988. doi:10.1137/0217058
    2. Róbert Szelepcsényi. The Method of Forced Enumeration for Nondeterministic Automata. Acta Informatica 26(3):279–284, 1988. doi:10.1007/BF00299636

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