On Resetting DLBA' s Oscar H. Ibarra Department of Computer Scienc e University of Californi a Santa Barbara, CA 9310 6 ibarra@cs.ucsb,edu A long-standing open problem in complexity theory is whether NSPACE(n) is equa l to DSPACE(n) . NSPACE(n) (DSPACE(n)) is the class of languages accepted b y linear-space nondeterministic (deterministic) multitape Turing machines . By Savitch's result [SAVI70], we know that NSPACE(n 1/2 ) is contained in DSPACE(n) . However, it is not known whether this result is optimal, i .e ., the following question i s open : 1) Is NSPACE(n 1/2 ) properly contained in DSPACE(n) ? From results of Chandra, Kozen and Stockmeyer [CHAN81], we also know tha t NSPACE(n 1/2 ) is contained in ATIME(n) and that ATIME(n) is contained i n DSPACE(n) . Here, ATIME(n) is the class of languages accepted by linear-time alternating multitape Turing machines . Again, the following question is open : 2) Is ATIME(n) properly contained in DSPACE(n) ? Note that if 2) were true, then 1) would also be true . Below, we suggest a way o f resolving question 2) in the affirmative by reducing it to a seemingly simpler, but stil l open, problem .
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On resetting DLBA's
Ibarra, Oscar H.
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, Volume 22 (1)
Association for Computing Machinery – Mar 1, 1991
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