The Immerman-Szelepcsenyi Theorem, proved independently by Neil Immerman and Robert Szelepcsenyi in 1987, states that nondeterministic space complexity classes are closed under complementation, so NSPACE of s(n) equals co-NSPACE of s(n) for any function s(n) of at least logarithmic size, and in particular that the class NL equals co-NL. The result resolved the long-standing second LBA problem and introduced the proof technique of inductive counting, and both authors received the 1995 Godel Prize for the work; no comparable result is known for time complexity classes.
Facts
StatementNondeterministic space complexity classes are closed under complementation: NSPACE(s(n)) = co-NSPACE(s(n)) for s(n) at least log n, in particular NL = co-NL. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Immerman-Szelepcsenyi theorem, Wikipedia
Sources
1. Immerman-Szelepcsenyi theorem, Wikipedia
Lead paragraph, statement
nondeterministic space complexity classes are closed under complementation.
Lead paragraph, attribution
was proven independently by Neil Immerman and Róbert Szelepcsényi in 1987.
- In Branch: Computational Complexity Theory, Lead sentence
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