Abstract
It is shown that a bounded language accepted by a nondeterministic Turing machine in spaceS(n ∈o(logn) can be accepted by a deterministic Turing machine in space MAX {(s(nn))2, logn}. This can be interpreted as extending Savitch's algorithm below logspace. Results of Alt can be used to show that in the general case the indicated space bound cannot be improved. The result can also be interpreted as a sharpening in the special case of bounded languages of the results of Monien and Sudborough.
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References
B. Monien, and I. H. Sudborough, On Eliminating Nondeterminism From Turing Machines Which Use Less Than Logarithm Worktape Space,Theoretical Computer Science, 21, 237–253, 1982.
H. Alt, Lower Bounds on Space Complexity for Context-Free Recognition,Acta Informatica, 12, 33–61, 1979.
W. Savitch, Relationships Between Nondeterministic and Deterministic Tape Complexities,J. Comp. System Sci., 4, 177–192, 1970.
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Litow, B.E. On efficient deterministic simulation of turing machine computations below logaspace. Math. Systems Theory 18, 11–18 (1985). https://doi.org/10.1007/BF01699458
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DOI: https://doi.org/10.1007/BF01699458