Abstract
The notion of linear-time computability is very sensitive to machine model. In this connection, we introduce a class NLT of functions computable in nearly linear time n(log n)O(1) on random access computers. NLT is very robust and does not depend on the particular choice of random access computers. Kolmogorov machines, Schönhage machines, random access Turing machines, etc., also compute exactly NLT functions in nearly linear time. It is not known whether usual multitape Turing machines are able to compute all NLT functions in nearly linear time. We do not believe they are and do not consider them necessarily appropriate for this relatively low complexity level. It turns out, however, that nondeterministic Turing machines accept exactly the languages in the nondeterministic version of NLT. We give also a machine-independent definition of NLT and a natural problem complete for NLT.
Partially supported by NSF grant DCR 85-03275 and by a grant from Binational US-Israel Science Foundation. A substantial portion of the work was done during a week in Fall 1985 when both authors visited Rutgers University; during the last stage of the work, the author was on a sabbatical visit to Stanford University and IBM Almaden Research Center.
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Gurevich, Y., Shelah, S. (1989). Nearly linear time. In: Meyer, A.R., Taitslin, M.A. (eds) Logic at Botik '89. Logic at Botik 1989. Lecture Notes in Computer Science, vol 363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51237-3_10
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DOI: https://doi.org/10.1007/3-540-51237-3_10
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