Nondeterministic Space is Closed Under Complementation

In this paper we show that nondeterministic space $s(n)$ is closed under complementation for $s(n)$ greater than or equal to $\log n$. It immediately follows that the context-sensitive languages are closed under complementation, thus settling a question raised by Kuroda [Inform. and Control, 7 (1964), pp. 207–233].

[1]  Neil Immerman,et al.  Languages that Capture Complexity Classes , 1987, SIAM J. Comput..

[2]  A. Meyer Review: Walter J. Savitch, Relationships between Nondeterministic and Deterministic Tape Complexities , 1974 .

[3]  Christos H. Papadimitriou,et al.  Symmetric Space-Bounded Computation , 1982, Theor. Comput. Sci..

[4]  Neil Immerman,et al.  Expressibility as a complexity measure: results and directions , 1987, SCT.

[5]  Peter S. Landweber Review: S.-Y. Kuroda, Classes of Languages and Linear-Bounded Automata , 1967 .

[6]  Allan Borodin,et al.  Two applications of complementation via inductive counting , 1988, [1988] Proceedings. Structure in Complexity Theory Third Annual Conference.

[7]  Stephen R. Mahaney Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[8]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[9]  Neil Immerman,et al.  Relational Queries Computable in Polynomial Time , 1986, Inf. Control..

[10]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[11]  Stephen A. Cook,et al.  A Taxonomy of Problems with Fast Parallel Algorithms , 1985, Inf. Control..

[12]  P. Strevens Iii , 1985 .

[13]  Patrick W. Dymond,et al.  The Log Space Oracle Hierarchy Collapses DRAFT , 1987 .

[14]  Seinosuke Toda Sigma_2 SPACE(n) is Closed under Complement , 1987, J. Comput. Syst. Sci..

[15]  S.-Y. Kuroda,et al.  Classes of Languages and Linear-Bounded Automata , 1964, Inf. Control..