If deterministic and nondeterministic space complexities are equal for log log n then they are also equal for log n
It is well known that for any „well behaved“ space function L(n) ≥ log n if DSPACE(L(n)) = NSPACE(L(n)) then also DSPACE(H(n)) = NSPACE(H(n)) for all „well behaved“ functions H(n) ≥ L(n). The aim of this paper is to show that also if DSPACE(log log n) = NSPACE(log log n) then L = NL (i.e. DSPACE(log n) = NSPACE(log n)).
Unable to display preview. Download preview PDF.
- 1.R. Freivalds, On the worktime of deterministic and nondeterministic Turing machines (in Russian). Latvijskij Matematiceskij Eshegodnik 23 (1979) 158–165.Google Scholar
- 2.R. Kannan, Alternation and the power of nondeterminism. 15-th STOC (1983) 344–346.Google Scholar
- 3.P. M. Lewis II, R. E. Stearns and J. Hartmanis, Memory bounds for the recognition of context-free and context-sensitive languages. IEEE Conf. Rec. on Switching Circuit Theory and Logical Design, NY (1965) 191–202.Google Scholar
- 4.B. Monien, On the LBA problem. LNCS 117, Fundamentals of Computation Theory, Proc. of 1981 International FCT-Conference, Szeged, Hungary, 1981 Springer Verlag Berlin, Heidelberg, New York 1981, 265–280.Google Scholar
- 5.W. Narkiewicz, Number Theory (translated by S. Kanemitsu). World Scientific Publishing Co. 1983.Google Scholar
- 6.W.J. Savitch, Relationships between nondeterministic and deterministic tape complexities. J. of Computer and System Sc., 4 (1970) 177–192.Google Scholar
- 7.M. Sipser, Halting space-bounded computations. TCS 10 (1980) 335–338.Google Scholar
- 7.A. Szepietowski, Remarks on languages acceptable in log log n space. IPL 27 (1988) 4, 201–203.Google Scholar