Abstract
It is shown that any nonderministic single-tape off-line Turing machine of time complexity T(n) can be speeded-up by one extra alternation by the factor log log T(n)/ √ log T(n), for any well-behaved function T(n). This leads to the separation NTIME1+I(T(n)) ⊂ σ 2 - TIME 1+I (T(n)) of the respective complexity classes. Analogous result holds also for the complementary classes co-NTIME1+I(T(n)) and π 2 - TIME1+I(T(n)). This is the first occasion where such separation results have been proved for a restricted type of multitape nondeterministic machines. For the general case of multitape nondeterministic machines similar results are not known to hold.
This research was supported by GA čR Grant No. 201/98/0717 and by an EU grant INCO-COOP 96-0195 ‘ALTEC-KIT’ jointly with the accompanying grant of the MMT R No. OK-304
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Wiedermann, J. (1998). Speeding-up nondeterministic single-tape off-line computations by one alternation. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055811
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