Abstract
A series of existing lower bound results for one-tape Turing machines (TM's) is extended to the strongest such model for the computation of functions: one-tape off-line TM's with a write-only output tape. (“Off-line” means: having a two-way input tape.) The following optimal lower bound is shown: Computing the transpose of Boolean ℓ×ℓ-matrices takes Ω(ℓ5/2)=Ω(n5/4) steps on such TM's. (n=ℓ2 is the length of the input.)
Written under partial support by NSF-grant DCR-8504247
This work is based on a part of the first author's Ph.D.-thesis at the University of Illinois at Chicago, Chicago, Illinois, U.S.A.
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References
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Dietzfelbinger, M., Maass, W. (1988). The complexity of matrix transposition on one-tape off-line turing machines with output tape. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_116
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DOI: https://doi.org/10.1007/3-540-19488-6_116
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