
PRAMs over integers do not compute maxflow efficiently
Finding lower bounds in complexity theory has proven to be an extremely ...
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SemiAlgebraic Proofs, IPS Lower Bounds and the τConjecture: Can a Natural Number be Negative?
We introduce the binary value principle which is a simple subsetsum ins...
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Lower Bounds on CrossEntropy Loss in the Presence of Testtime Adversaries
Understanding the fundamental limits of robust supervised learning has e...
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New Bounds for the Vertices of the Integer Hull
The vertices of the integer hull are the integral equivalent to the well...
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Inferring Lower Runtime Bounds for Integer Programs
We present a technique to infer lower bounds on the worstcase runtime c...
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On the best constants in L^2 approximation
In this paper we provide explicit upper and lower bounds on the L^2nwid...
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On the I/O complexity of hybrid algorithms for Integer Multiplication
Almost asymptotically tight lower bounds are derived for the I/O complex...
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Lower bounds for prams over Z
This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological entropy for dynamical systems, the method captures four previous lower bounds results from the literature in algebraic complexity. Among these results lies Mulmuley's proof that "prams without bit operations" do not compute the maxflow problem in polylogarithmic time, which was the best known lower bounds in the quest for a proof that NC = Ptime. Inspired from a refinement of Steele and Yao's lower bounds, due to BenOr, we strengthen Mulmuley's result to a larger class of machines, showing that prams over integer do not compute maxflow in polylogarithmic time.
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