198,558 research outputs found
A Direct Product Theorem for One-Way Quantum Communication
No full textWe prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation f ⊆ ××. For any 0 < ε < δ < 1/2 and any k≥1, we show that
Q¹_{1-(1-ε)^{Ω(k/log||)}}(f^k) = Ω(k⋅Q¹_{δ}(f)),
where Q¹_{ε}(f) represents the one-way entanglement-assisted quantum communication complexity of f with worst-case error ε and f^k denotes k parallel instances of f.
As far as we are aware, this is the first direct product theorem for the quantum communication complexity of a general relation - direct sum theorems were previously known for one-way quantum protocols for general relations, while direct product theorems were only known for special cases. Our techniques are inspired by the parallel repetition theorems for the entangled value of two-player non-local games, under product distributions due to Jain, Pereszlényi and Yao [Rahul Jain et al., 2014], and under anchored distributions due to Bavarian, Vidick and Yuen [Bavarian et al., 2017], as well as message compression for quantum protocols due to Jain, Radhakrishnan and Sen [Rahul Jain et al., 2005]. In particular, we show that a direct product theorem holds for the distributional one-way quantum communication complexity of f under any distribution q on × that is anchored on one side, i.e., there exists a y^* such that q(y^*) is constant and q(x|y^*) = q(x) for all x. This allows us to show a direct product theorem for general distributions, since for any relation f and any distribution p on its inputs, we can define a modified relation f̃ which has an anchored distribution q close to p, such that a protocol that fails with probability at most ε for f̃ under q can be used to give a protocol that fails with probability at most ε + ζ for f under p.
Our techniques also work for entangled non-local games which have input distributions anchored on any one side, i.e., either there exists a y^* as previously specified, or there exists an x^* such that q(x^*) is constant and q(y|x^*) = q(y) for all y. In particular, we show that for any game G = (q, ×, ×ℬ, ) where q is a distribution on × anchored on any one side with constant anchoring probability, then
ω^*(G^k) = (1 - (1-ω^*(G))⁵) ^{Ω(k/(log(||⋅|ℬ|)))}
where ω^*(G) represents the entangled value of the game G. This is a generalization of the result of [Bavarian et al., 2017], who proved a parallel repetition theorem for games anchored on both sides, i.e., where both a special x^* and a special y^* exist, and potentially a simplification of their proof
Maradana rogueti P. Leraut 2015
No full text430. Maradana rogueti P. Leraut, 2015: 38, figs 2, 21 Type locality: Tamil Nadu, Viluppuram Dt, Thely Distribution. Indian records: Inde, Tamil Nadu (P. Leraut 2015). Global records: unknown.Published as part of Singh, Navneet, Ranjan, Rahul, Talukdar, Avishek, Joshi, Rahul, Kirti, Jagbir Singh, Chandra, Kailash & Mally, Richard, 2022, A catalogue of Indian Pyraloidea (Lepidoptera), pp. 1-423 in Zootaxa 5197 (1) on page 129, DOI: 10.11646/zootaxa.5197.1.1, http://zenodo.org/record/725229
Third World Protest: Between Home and The World, Rahul Rao
No full textRAO, Rahul. Third World Protest: Between Home and the World, 2010. Oxford University Press, USA, 288 p. (ISBN 0199560374).RAO, Rahul. Third World Protest: Between Home and the World, 2010. Oxford University Press, USA, 288 p. (ISBN 0199560374)
Technology strategy in defense industry acquisitions : a comparative assessment of two giants
No full text"August 1997."Includes bibliographical references (p. 23-24).Rahul N. Advani ... [et al.
Scoparia indica P. Leraut 1986
No full text<p> <b> 536. <i>Scoparia indica</i> P. Leraut, 1986: 128</b> </p> <p>Type locality: India, Uttar Pradesh, Mussoorie, Himalaya, 1500–2200 m</p> <p>Distribution. Indian records: Uttar Pradesh, Mussoorie, Himalaya (P. Leraut 1986). Global records: unknown.</p>Published as part of <i>Singh, Navneet, Ranjan, Rahul, Talukdar, Avishek, Joshi, Rahul, Kirti, Jagbir Singh, Chandra, Kailash & Mally, Richard, 2022, A catalogue of Indian Pyraloidea (Lepidoptera), pp. 1-423 in Zootaxa 5197 (1)</i> on page 244, DOI: 10.11646/zootaxa.5197.1.1, <a href="http://zenodo.org/record/7252292">http://zenodo.org/record/7252292</a>
RAO, Rahul. Out of Time: The Queer Politics of Postcoloniality. New York: Oxford University Press, 2020. 262 p. Resenha
No full textResenha: RAO, Rahul. Out of Time: The Queer Politics of Postcoloniality. 1. ed.New York: Oxford University Press, 2020. 262 p
Approaching MCSP from Above and Below: Hardness for a Conditional Variant and AC^0[p]
No full textThe Minimum Circuit Size Problem (MCSP) asks whether a given Boolean function has a circuit of at most a given size. MCSP has been studied for over a half-century and has deep connections throughout theoretical computer science including to cryptography, computational learning theory, and proof complexity. For example, we know (informally) that if MCSP is easy to compute, then most cryptography can be broken. Despite this cryptographic hardness connection and extensive research, we still know relatively little about the hardness of MCSP unconditionally. Indeed, until very recently it was unknown whether MCSP can be computed in AC^0[2] (Golovnev et al., ICALP 2019).
Our main contribution in this paper is to formulate a new "oracle" variant of circuit complexity and prove that this problem is NP-complete under randomized reductions. In more detail, we define the Minimum Oracle Circuit Size Problem (MOCSP) that takes as input the truth table of a Boolean function f, a size threshold s, and the truth table of an oracle Boolean function O, and determines whether there is a circuit with O-oracle gates and at most s wires that computes f. We prove that MOCSP is NP-complete under randomized polynomial-time reductions.
We also extend the recent AC^0[p] lower bound against MCSP by Golovnev et al. to a lower bound against the circuit minimization problem for depth-d formulas, (AC^0_d)-MCSP. We view this result as primarily a technical contribution. In particular, our proof takes a radically different approach from prior MCSP-related hardness results
Recensió d'Out of Time. The Queer Politics of Postcoloniality de Rahul Rao
No full textObra ressenyada: Rahul RAO, Out of time. The queer politics of postcoloniality. Oxford Press, 2020
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
On the structure of learnability beyond P/poly
No full textMotivated by the goal of showing stronger structural results about the complexity of learning, we study the learnability of strong concept classes beyond P/poly, such as PSPACE/poly and EXP/poly. We show the following:
1) (Unconditional Lower Bounds for Learning) Building on [Adam R. Klivans et al., 2013], we prove unconditionally that BPE/poly cannot be weakly learned in polynomial time over the uniform distribution, even with membership and equivalence queries.
2) (Robustness of Learning) For the concept classes EXP/poly and PSPACE/poly, we show unconditionally that worst-case and average-case learning are equivalent, that PAC-learnability and learnability over the uniform distribution are equivalent, and that membership queries do not help in either case.
3) (Reducing Succinct Search to Decision for Learning) For the decision problems R_{Kt} and R_{KS} capturing the complexity of learning EXP/poly and PSPACE/poly respectively, we show a succinct search to decision reduction: for each of these problems, the problem is in BPP iff there is a probabilistic polynomial-time algorithm computing circuits encoding proofs for positive instances of the problem. This is shown via a more general result giving succinct search to decision results for PSPACE, EXP and NEXP, which might be of independent interest.
4) (Implausibility of Oblivious Strongly Black-Box Reductions showing NP-hardness of learning NP/poly) We define a natural notion of hardness of learning with respect to oblivious strongly black-box reductions. We show that learning PSPACE/poly is PSPACE-hard with respect to oblivious strongly black-box reductions. On the other hand, if learning NP/poly is NP-hard with respect to oblivious strongly black-box reductions, the Polynomial Hierarchy collapses
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