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Nondeterministic space is closed under complementation. (English) Zbl 0668.68056
A break-through result is proved: all nondeterministic space complexity classes are closed under complementation. In symbols: $$NSPACE(s(n))=co$$- NSPACE(s(n)). As the special case $$s(n)=n$$ one obtains that the context- sensitive languages (the LBA languages) are closed under complementation, answering a well-known open problem by Kuroda from 1964. The proof is astonishingly simple, it uses a nondeterministic, inductive counting technique.
The result was independently and at the same time shown by R. Szelepcsényi in the Bulletin of the EATCS 33, 96-100 (1987; Zbl 0664.68082).

##### MSC:
 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 68Q25 Analysis of algorithms and problem complexity 03D15 Complexity of computation (including implicit computational complexity)
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