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Immerman-Szelepcsenyi Theorem

Logic and Foundations

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
Statement
Nondeterministic 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
Proof Year
1987 1
Classification
Statement Form
Inequality 1
Statement Form
Identity or Equation 1
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.
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