Immerman, Neil Nondeterministic space is closed under complementation. (English) Zbl 0668.68056 SIAM J. Comput. 17, No. 5, 935-938 (1988). 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). Cited in 9 ReviewsCited in 211 Documents MSC: 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 68Q25 Analysis of algorithms and problem complexity 03D15 Complexity of computation (including implicit computational complexity) Keywords:nondeterminism; complexity classes; space complexity; context-sensitive languages Citations:Zbl 0664.68082 PDFBibTeX XMLCite \textit{N. Immerman}, SIAM J. Comput. 17, No. 5, 935--938 (1988; Zbl 0668.68056) Full Text: DOI Link