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On f-sparse sets in NP - P

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SOFSEM'97: Theory and Practice of Informatics (SOFSEM 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1338))

Abstract

In this paper a new upward separation technique is developed. One of its consequences solves an open question of Hartmanis [6]: There is an O (n log n)-sparse set in NP − P iff

$$\bigcup\limits_{c > 1} {NTIME\left( {2^{c\sqrt n } } \right) \ne } \bigcup\limits_{c > 1} {DTIME} \left( {2^{c\sqrt n } } \right).$$

The technique is similar to that ones proving that any sparse set is conjunctively truth-table reducible to a tally set (by Buhrman, Longpré and Spaan

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References

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Author information

Authors and Affiliations

  1. Charles University, Prague, Czech Republic

    Vladimír Glasnák

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  1. Vladimír Glasnák
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František Plášil Keith G. Jeffery

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© 1997 Springer-Verlag Berlin Heidelberg

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Glasnák, V. (1997). On f-sparse sets in NP - P. In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_121

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  • DOI: https://doi.org/10.1007/3-540-63774-5_121

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63774-5

  • Online ISBN: 978-3-540-69645-2

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