Abstract
For nondeterministic Turing machines with one work-tape and one-way input a lower time bound Ω(m 2ℓ) on sorting m strings of length ℓ each is shown, which matches the upper bound. For the related Element Distinctness Problem with input of the same format we prove the upper bound O(m 2) if ℓ = O(m/logm), showing this problem to be easier than sorting. The bound O(m 2) also holds for deterministic machines if ℓ = c + logm with constant c. For this problem Szepietowski has shown the bound Θ(m 2logm) on deterministic Turing machines without input tape.
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Petersen, H. (2008). Sorting and Element Distinctness on One-Way Turing Machines. In: Martín-Vide, C., Otto, F., Fernau, H. (eds) Language and Automata Theory and Applications. LATA 2008. Lecture Notes in Computer Science, vol 5196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88282-4_39
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DOI: https://doi.org/10.1007/978-3-540-88282-4_39
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