A Short Counterexample Property for Safety and Liveness Verification of Fault-tolerant Distributed Algorithms

Distributed algorithms have many mission-critical applications ranging from embedded systems and replicated databases to cloud computing. Due to asynchronous communication, process faults, or network failures, these algorithms are difficult to design and verify. Many algorithms achieve fault tolerance by using threshold guards that, for instance, ensure that a process waits until it has received an acknowledgment from a majority of its peers. Consequently, domain-specific languages for fault-tolerant distributed systems offer language support for threshold guards. We introduce an automated method for model checking of safety and liveness of threshold-guarded distributed algorithms in systems where the number of processes and the fraction of faulty processes are parameters. Our method is based on a short counterexample property: if a distributed algorithm violates a temporal specification (in a fragment of LTL), then there is a counterexample whose length is bounded and independent of the parameters. We prove this property by (i) characterizing executions depending on the structure of the temporal formula, and (ii) using commutativity of transitions to accelerate and shorten executions. We extended the ByMC toolset (Byzantine Model Checker) with our technique, and verified liveness and safety of 10 prominent fault-tolerant distributed algorithms, most of which were out of reach for existing techniques.Comment: 16 pages, 11 pages appendi

Approximate Consensus in Highly Dynamic Networks: The Role of Averaging Algorithms

In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate consensus is solvable if and only if the communication graph in each round has a rooted spanning tree, i.e., there is a coordinator at each time. The striking point in this result is that the coordinator is not required to be unique and can change arbitrarily from round to round. Interestingly, the class of averaging algorithms, which are memoryless and require no process identifiers, entirely captures the solvability issue of approximate consensus in that the problem is solvable if and only if it can be solved using any averaging algorithm. Concerning the time complexity of averaging algorithms, we show that approximate consensus can be achieved with precision of $\varepsilon$ in a coordinated network model in $O(n^{n+1} \log\frac{1}{\varepsilon})$ synchronous rounds, and in $O(\Delta n^{n\Delta+1} \log\frac{1}{\varepsilon})$ rounds when the maximum round delay for a message to be delivered is $\Delta$. While in general, an upper bound on the time complexity of averaging algorithms has to be exponential, we investigate various network models in which this exponential bound in the number of nodes reduces to a polynomial bound. We apply our results to networked systems with a fixed topology and classical benign fault models, and deduce both known and new results for approximate consensus in these systems. In particular, we show that for solving approximate consensus, a complete network can tolerate up to 2n-3 arbitrarily located link faults at every round, in contrast with the impossibility result established by Santoro and Widmayer (STACS '89) showing that exact consensus is not solvable with n-1 link faults per round originating from the same node

Iterative Approximate Consensus in the presence of Byzantine Link Failures

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed communication links, but the nodes are assumed to be fault-free. Recent work has addressed the problem of reaching approximate consen- sus in incomplete graphs with Byzantine nodes using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations [22, 21, 23, 12]. However, to the best of our knowledge, we are the first to consider approximate consensus in the presence of Byzan- tine links. We extend our past work that provided exact characterization of graphs in which the iterative approximate consensus problem in the presence of Byzantine node failures is solvable [22, 21]. In particular, we prove a tight necessary and sufficient condition on the underlying com- munication graph for the existence of iterative approximate consensus algorithms under transient Byzantine link model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609

Combined Untargeted and Targeted Fingerprinting by Comprehensive Two-Dimensional Gas Chromatography to Track Compositional Changes on Hazelnut Primary Metabolome during Roasting

This study focuses on the detectable metabolome of high-quality raw hazelnuts (Cory- lus avellana L.) and on its changes after dry-roasting. Informative fingerprinting was obtained by comprehensive two-dimensional gas chromatography with fast-scanning quadrupole mass spectrom- etry (GC×GC-qMS) combined with dedicated data processing. In particular, combined untargeted and targeted (UT) fingerprinting, based on pattern recognition by template matching, is applied to chromatograms from raw and roasted samples of Tonda Gentile Trilobata and Anakliuri hazelnuts harvested in Italy and Georgia. Lab-scale roasting was designed to develop a desirable organoleptic profile matching industrial standards. Results, based on 430 peak features, reveal that phenotype expression is markedly correlated to cultivar and pedoclimatic conditions. Discriminant components between cultivars are amino acids (valine, alanine, glycine, and proline); organic acids (citric, aspartic, malic, gluconic, threonic, and 4-aminobutanoic acids); and sugars and polyols (maltose, xylulose, xylitol, turanose, mannitol, scyllo-inositol, and pinitol). Of these, alanine, glycine, and proline have a high informational role as precursors of 2-acetyl- and 2-propionylpyrroline, two key-aroma com- pounds of roasted hazelnuts. Roasting has a decisive impact on metabolite patterns—it caused a marked decrease (−90%) of alanine, proline, leucine and valine, and aspartic and pyroglutamic acid and a −50% reduction of saccharose and galactose

Quantum computing in optical microtraps based on the motional states of neutral atoms

We investigate quantum computation with neutral atoms in optical microtraps where the qubit is implemented in the motional states of the atoms, i.e., in the two lowest vibrational states of each trap. The quantum gate operation is performed by adiabatically approaching two traps and allowing tunneling and cold collisions to take place. We demonstrate the capability of this scheme to realize a square-root of swap gate, and address the problem of double occupation and excitation to other unwanted states. We expand the two-particle wavefunction in an orthonormal basis and analyze quantum correlations throughout the whole gate process. Fidelity of the gate operation is evaluated as a function of the degree of adiabaticity in moving the traps. Simulations are based on rubidium atoms in state-of-the-art optical microtraps with quantum gate realizations in the few tens of milliseconds duration range.Comment: 11 pages, 7 figures, for animations of the gate operation, see http://www.itp.uni-hannover.de/~eckert/na/index.htm

Ubiquitination and degradation of the hominoid- specific oncoprotein TBC1D3 Is mediated by CUL7 E3 ligase

Expression of the hominoid-specific TBC1D3 oncoprotein enhances growth factor receptor signaling and subsequently promotes cellular proliferation and survival. Here we report that TBC1D3 is degraded in response to growth factor signaling, suggesting that TBC1D3 expression is regulated by a growth factor-driven negative feedback loop. To gain a better understanding of how TBC1D3 is regulated, we studied the effects of growth factor receptor signaling on TBC1D3 post-translational processing and turnover. Using a yeast two-hybrid screen, we identified CUL7, the scaffolding subunit of the CUL7 E3 ligase complex, as a TBC1D3-interacting protein. We show that CUL7 E3 ligase ubiquitinates TBC1D3 in response to serum stimulation. Moreover, TBC1D3 recruits F-box 8 (Fbw8), the substrate recognition domain of CUL7 E3 ligase, in pull-down experiments and in an in vitro assay. Importantly, alkaline phosphatase treatment of TBC1D3 suppresses its ability to recruit Fbw8, indicating that TBC1D3 phosphorylation is critical for its ubiquitination and degradation. We conclude that serum- and growth factor-stimulated TBC1D3 ubiquitination and degradation are regulated by its interaction with CUL7-Fbw8

Single Atom Cooling by Superfluid Immersion: A Non-Destructive Method for Qubits

We present a scheme to cool the motional state of neutral atoms confined in sites of an optical lattice by immersing the system in a superfluid. The motion of the atoms is damped by the generation of excitations in the superfluid, and under appropriate conditions the internal state of the atom remains unchanged. This scheme can thus be used to cool atoms used to encode a series of entangled qubits non-destructively. Within realisable parameter ranges, the rate of cooling to the ground state is found to be sufficiently large to be useful in experiments.Comment: 14 pages, 9 figures, RevTeX

Quantum computing implementations with neutral particles

We review quantum information processing with cold neutral particles, that is, atoms or polar molecules. First, we analyze the best suited degrees of freedom of these particles for storing quantum information, and then we discuss both single- and two-qubit gate implementations. We focus our discussion mainly on collisional quantum gates, which are best suited for atom-chip-like devices, as well as on gate proposals conceived for optical lattices. Additionally, we analyze schemes both for cold atoms confined in optical cavities and hybrid approaches to entanglement generation, and we show how optimal control theory might be a powerful tool to enhance the speed up of the gate operations as well as to achieve high fidelities required for fault tolerant quantum computation.Comment: 19 pages, 12 figures; From the issue entitled "Special Issue on Neutral Particles

Paxos Consensus, Deconstructed and Abstracted (Extended Version)

Lamport's Paxos algorithm is a classic consensus protocol for state machine replication in environments that admit crash failures. Many versions of Paxos exploit the protocol's intrinsic properties for the sake of gaining better run-time performance, thus widening the gap between the original description of the algorithm, which was proven correct, and its real-world implementations. In this work, we address the challenge of specifying and verifying complex Paxos-based systems by (a) devising composable specifications for implementations of Paxos's single-decree version, and (b) engineering disciplines to reason about protocol-aware, semantics-preserving optimisations to single-decree Paxos. In a nutshell, our approach elaborates on the deconstruction of single-decree Paxos by Boichat et al. We provide novel non-deterministic specifications for each module in the deconstruction and prove that the implementations refine the corresponding specifications, such that the proofs of the modules that remain unchanged can be reused across different implementations. We further reuse this result and show how to obtain a verified implementation of Multi-Paxos from a verified implementation of single-decree Paxos, by a series of novel protocol-aware transformations of the network semantics, which we prove to be behaviour-preserving.Comment: Accepted for publication in the 27th European Symposium on Programming (ESOP'18

Matter-wave interferometry in a double well on an atom chip

Matter-wave interference experiments enable us to study matter at its most basic, quantum level and form the basis of high-precision sensors for applications such as inertial and gravitational field sensing. Success in both of these pursuits requires the development of atom-optical elements that can manipulate matter waves at the same time as preserving their coherence and phase. Here, we present an integrated interferometer based on a simple, coherent matter-wave beam splitter constructed on an atom chip. Through the use of radio-frequency-induced adiabatic double-well potentials, we demonstrate the splitting of Bose-Einstein condensates into two clouds separated by distances ranging from 3 to 80 microns, enabling access to both tunnelling and isolated regimes. Moreover, by analysing the interference patterns formed by combining two clouds of ultracold atoms originating from a single condensate, we measure the deterministic phase evolution throughout the splitting process. We show that we can control the relative phase between the two fully separated samples and that our beam splitter is phase-preserving