Super-linear time-space tradeoff lower bounds for randomized computation

Beame, Paul; Saks, Michael; Sun, Xi; Vee, Erik

doi:10.1109/sfcs.2000.892078

Cited by 48 publications

(43 citation statements)

References 16 publications

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“…Since then, the main result of this paper was further improved by Beame, Saks, Sun, and Vee in [7] by making the time/space lower bounds sharper and generalizing the theorem for the case of probabilistic branching programs. Their proofs use the results and techniques of the present paper (together with methods of different nature).…”

Section: Subsequent Developmentsmentioning

confidence: 94%

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Ajtai¹

2005

Theory of Comput.

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Section: Subsequent Developmentsmentioning

confidence: 94%

“…., l} with this property. Then (7). the probability of the event that we get equalities for every element of this set is at most…”

Section: Partitioning the Rows And Columnsmentioning

confidence: 99%

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Ajtai¹

2005

Theory of Comput.

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“…Is element distinctness really as hard as sorting classically? Note that strong classical tradeoffs are known for element distinctness if only a comparison oracle is used [8,21], but the best tradeoff known for general models is T = Ω(n log(n/S)), given in [4], no better product tradeoff than ST = Ω(n log 2 n). A quantum query lower bound of Ω(n 2/3 ) has recently been shown by Shi [20].…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Quantum time-space tradeoffs for sorting

Klauck

2003

Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing

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We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant factor in time complexity, this is wrong in a space bounded setting. We observe that for all storage bounds n/ log n ≥ S ≥ log 3 n, one can devise a quantum algorithm that sorts n numbers (using comparisons only) in time T = O(n 3/2 log 3/2 n/ √ S). We then show the following lower bound on the time-space tradeoff for sorting n numbers from a polynomial size range in a general sorting algorithm (not necessarily based on comparisons): T S = Ω(n 3/2 ). Hence for small values of S the upper bound is almost tight. Classically the time-space tradeoff for sorting is T S = Θ(n 2 ).

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“…The possibility of assumption free memory-bound functions: For the memory-bound functions an intriguing possibility is to apply recent results from complexity theory in order to be able to make unconditional (not relying on any assumptions) statements about proposed schemes. One of the more promising directions in recent years is the work on lower bounds for branching program and the RAM model by Ajtai [3,4] and Beame et al [6]. It is not clear how to directly apply such results.…”

Section: Open Problems In Moderately Hard Functionsmentioning

confidence: 99%

Moderately Hard Functions: From Complexity to Spam Fighting

Naor

2003

Lecture Notes in Computer Science

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Abstract.A key idea in cryptography is using hard functions in order to obtain secure schemes. The theory of hard functions (e.g. one-way functions) has been a great success story, and the community has developed a fairly strong understanding of what types of cryptographic primitives can be achieved under which assumption. We explore the idea of using moderately hard functions in order to achieve many tasks for which a perfect solution is impossible, for instance, denial-of-service. We survey some of the applications of such functions and in particular describe the properties moderately hard functions need for fighting unsolicited electronic mail. We suggest several research directions and (re)call for the development of a theory of such functions.

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Super-linear time-space tradeoff lower bounds for randomized computation

Cited by 48 publications

References 16 publications

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Quantum time-space tradeoffs for sorting

Moderately Hard Functions: From Complexity to Spam Fighting

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