Bloom Filters in Adversarial Environments

Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are independent of the internal randomness of the data structure. In this work, we consider data structures in a more robust model, which we call the adversarial model. Roughly speaking, this model allows an adversary to choose inputs and queries adaptively according to previous responses. Specifically, we consider a data structure known as "Bloom filter" and prove a tight connection between Bloom filters in this model and cryptography. A Bloom filter represents a set $S$ of elements approximately, by using fewer bits than a precise representation. The price for succinctness is allowing some errors: for any $x \in S$ it should always answer `Yes', and for any $x \notin S$ it should answer `Yes' only with small probability. In the adversarial model, we consider both efficient adversaries (that run in polynomial time) and computationally unbounded adversaries that are only bounded in the number of queries they can make. For computationally bounded adversaries, we show that non-trivial (memory-wise) Bloom filters exist if and only if one-way functions exist. For unbounded adversaries we show that there exists a Bloom filter for sets of size $n$ and error $\varepsilon$, that is secure against $t$ queries and uses only $O(n \log{\frac{1}{\varepsilon}}+t)$ bits of memory. In comparison, $n\log{\frac{1}{\varepsilon}}$ is the best possible under a non-adaptive adversary

Baryon Number Transport via Gluonic Junctions

A novel non-perturbative gluon junction mechanism is introduced within the HIJING/B nuclear collision event generator to calculate baryon number transport and hyperon production in pA and AA collisions. This gluonic mechanism can account for the observed large mid-rapidity valence baryon yield in Pb+Pb at 160 AGeV and predicts high initial baryon densities at RHIC. However, the highly enhanced Lambda-Lambdabar yield and the baryon transverse momentum flow observed in this reaction can only be partially described.Comment: 9 pages, 3 figures, corrected typos and revised conten

THE VIRTUE OF COMPROMISE

O compromisso é a virtude dos agentes políticos. Esta imagem do político é comum e familiar: a política é o domínio onde os políticos razoáveis e capazes de chegar a compromissos resolvem problemas, e onde os políticos pouco razoáveis e não dispostos a chegar a compromissos são relegados para as margens. Assim, é sempre correcto e razoável chegar a bons compromissos. Neste artigo, argumento que, sob certas condições, é melhor e mais eficaz ter políticos que não fazem compromissos. Por exemplo, pensemos num partido político que a cada eleição se move mais para o centro do espectro político para maximizar as suas probabilidades de ganhar, mas perde as eleições e isto à custa do crescente distanciamento do centro político em relação às suas posições originais. Se o processo se repetir, então uma série de compromissos seria desastrosa, tanto quanto as considerações do auto-torturador são desastrosas. Assim, há algumas formas sistemáticas através das quais os compromissos de um político virtuoso não são (em última análise) virtuosos. Frequentemente, a virtude política é autodestrutiva, e é por isso uma maldição disfarçada.Compromise is the virtue of political agents. This picture of the political is as common and familiar: politics is a realm where the reasonable, the compromising politicians get things done and the unreasonable and uncompromising are doomed to fringes. Thus, it is always right and reasonable make good compromises. The paper argues that under certain conditions, it is better and more effective to have non-compromising politicians. For example, think of a political party that every election moves towards the political center to maximize its chances of winning, but loses the elections at the cost of having the political center move further away from its original positions. If the process repeats itself, then a series of compromise would be disastrous, much as the considerations of the self-torturer are disastrous. Thus, there are systematic ways in which the reasonable compromises of a virtuous politician are sometimes (ultimately) unreasonable. Political virtue is all too often self-defeating, and therefore a curse in disguise

Design and Construction of the 3.2 Mev High Voltage Column for Darht II

A 3.2 MeV injector has been designed and built for the Darht II Project at Los Alamos Lab. The installation of the complete injector system is nearing completion at this time. The requirements for the injector are to produce a 3.2 MeV, 2000 ampere electron pulse with a flattop width of at least 2-microseconds and emittance of less than 0.15 p cm-rad normalized. A large high voltage column has been built and installed. The column is vertically oriented, is 4.4 meters long, 1.2 meters in diameter, and weights 5700 kilograms. A novel method of construction has been employed which utilizes bonded mycalex insulating rings. This paper will describe the design, construction, and testing completed during construction. Mechanical aspects of the design will be emphasized.Comment: 3 pages, 4 figures, Linac 200

The Journey from NP to TFNP Hardness

The class TFNP is the search analog of NP with the additional guarantee that any instance has a solution. TFNP has attracted extensive attention due to its natural syntactic subclasses that capture the computational complexity of important search problems from algorithmic game theory, combinatorial optimization and computational topology. Thus, one of the main research objectives in the context of TFNP is to search for efficient algorithms for its subclasses, and at the same time proving hardness results where efficient algorithms cannot exist. Currently, no problem in TFNP is known to be hard under assumptions such as NP hardness, the existence of one-way functions, or even public-key cryptography. The only known hardness results are based on less general assumptions such as the existence of collision-resistant hash functions, one-way permutations less established cryptographic primitives (e.g. program obfuscation or functional encryption). Several works explained this status by showing various barriers to proving hardness of TFNP. In particular, it has been shown that hardness of TFNP hardness cannot be based on worst-case NP hardness, unless NP=coNP. Therefore, we ask the following question: What is the weakest assumption sufficient for showing hardness in TFNP? In this work, we answer this question and show that hard-on-average TFNP problems can be based on the weak assumption that there exists a hard-on-average language in NP. In particular, this includes the assumption of the existence of one-way functions. In terms of techniques, we show an interesting interplay between problems in TFNP, derandomization techniques, and zero-knowledge proofs

Congested Clique Algorithms for Graph Spanners

Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling schemes and routing to solving linear systems and spectral sparsification. A k-spanner maintains pairwise distances up to multiplicative factor of k. It is a folklore that for every n-vertex graph G, one can construct a (2k-1) spanner with O(n^{1+1/k}) edges. In a distributed setting, such spanners can be constructed in the standard CONGEST model using O(k^2) rounds, when randomization is allowed. In this work, we consider spanner constructions in the congested clique model, and show: - a randomized construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k) rounds. The previous best algorithm runs in O(k) rounds; - a deterministic construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k +(log log n)^3) rounds. The previous best algorithm runs in O(k log n) rounds. This improvement is achieved by a new derandomization theorem for hitting sets which might be of independent interest; - a deterministic construction of a O(k)-spanner with O(k * n^{1+1/k}) edges in O(log k) rounds