Abstract
We show that for all reals c and d such that c 2 d < 4 there exists a real e > 0 such that tautologies of length n cannot be decided by both a nondeterministic algorithm that runs in time n c, and a nondeterministic algorithm that runs in time n d and space n e. In particular, for all \(d < \sqrt[3]{4}\) there exists an e > 0 such that tautologies cannot be decided by a nondeterministic algorithm that runs in time n d and space n e.
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References
Fortnow, L.: Time-space tradeoffs for satisfiability. Journal of Computer and System Sciences 60, 337–353 (2000)
Fortnow, L., Lipton, R., van Melkebeek, D., Viglas, A.: Time-space lower bounds for satisfiability. Journal of the ACM 52, 835–865 (2005)
Fortnow, L., van Melkebeek, D.: Time-space tradeoffs for nondeterministic computation. In: Proceedings of the 15th IEEE Conference on Computational Complexity, pp. 2–13. IEEE, Los Alamitos (2000)
van Melkebeek, D.: A survey of lower bounds for satisfiability and related problems. Foundations and Trends in Theoretical Computer Science 2, 197–303 (2007)
Savitch, W.: Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences 4, 177–192 (1970)
Williams, R.: Time-space tradeoffs for counting NP solutions modulo integers. Computational Complexity 17, 179–219 (2008)
Williams, R.: Alternation-trading proofs, linear programming, and lower bounds (manuscript, 2009)
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Diehl, S., van Melkebeek, D., Williams, R. (2009). An Improved Time-Space Lower Bound for Tautologies. In: Ngo, H.Q. (eds) Computing and Combinatorics. COCOON 2009. Lecture Notes in Computer Science, vol 5609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02882-3_43
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DOI: https://doi.org/10.1007/978-3-642-02882-3_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02881-6
Online ISBN: 978-3-642-02882-3
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