Folding of Hyperbolic Manifolds

Abstract In this paper, we introduce the definition of hyperbolic manifold. The folding of hyperbolic manifold into itself is defined and discussed. Types of these foldings are deduced. Theorems governing these types are achieved. Mathematics Subject Classification, 51H10, 57N2

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

Pessimistic Software Lock-Elision

Read-write locks are one of the most prevalent lock forms in concurrent applications because they allow read accesses to locked code to proceed in parallel. However, they do not offer any parallelism between reads and writes. This paper introduces pessimistic lock-elision (PLE), a new approach for non-speculatively replacing read-write locks with pessimistic (i.e. non-aborting) software transactional code that allows read-write concurrency even for contended code and even if the code includes system calls. On systems with hardware transactional support, PLE will allow failed transactions, or ones that contain system calls, to preserve read-write concurrency. Our PLE algorithm is based on a novel encounter-order design of a fully pessimistic STM system that in a variety of benchmarks spanning from counters to trees, even when up to 40% of calls are mutating the locked structure, provides up to 5 times the performance of a state-of-the-art read-write lock.National Science Foundation (U.S.) (Grant 1217921

How Many Cooks Spoil the Soup?

In this work, we study the following basic question: "How much parallelism does a distributed task permit?" Our definition of parallelism (or symmetry) here is not in terms of speed, but in terms of identical roles that processes have at the same time in the execution. We initiate this study in population protocols, a very simple model that not only allows for a straightforward definition of what a role is, but also encloses the challenge of isolating the properties that are due to the protocol from those that are due to the adversary scheduler, who controls the interactions between the processes. We (i) give a partial characterization of the set of predicates on input assignments that can be stably computed with maximum symmetry, i.e., $\Theta(N_{min})$, where $N_{min}$ is the minimum multiplicity of a state in the initial configuration, and (ii) we turn our attention to the remaining predicates and prove a strong impossibility result for the parity predicate: the inherent symmetry of any protocol that stably computes it is upper bounded by a constant that depends on the size of the protocol.Comment: 19 page

ByMC: Byzantine Model Checker

International audienceIn recent work [12,10], we have introduced a technique for automatic verification of threshold-guarded distributed algorithms that have the following features: (1) up to t of processes may crash or behave Byzantine; (2) the correct processes count messages and progress when they receive sufficiently many messages, e.g., at least t + 1; (3) the number n of processes in the system is a parameter, as well as t; (4) and the parameters are restricted by a resilience condition, e.g., n > 3t.In this paper, we present Byzantine Model Checker that implements the above-mentioned technique. It takes two kinds of inputs, namely, (i) threshold automata (the framework of our verification techniques) or (ii) Parametric Promela (which is similar to the way in which the distributed algorithms were described in the literature).We introduce a parallel extension of the tool, which exploits the parallelism enabled by our technique on an MPI cluster. We compare performance of the original technique and of the extensions by verifying 10 benchmarks that model fault-tolerant distributed algorithms from the literature. For each benchmark algorithm we check two encodings: a manual encoding in threshold automata vs. a Promela encoding

“Genes”

In order to describe a cell at molecular level, a notion of a “gene” is neither necessary nor helpful. It is sufficient to consider the molecules (i.e., chromosomes, transcripts, proteins) and their interactions to describe cellular processes. The downside of the resulting high resolution is that it becomes very tedious to address features on the organismal and phenotypic levels with a language based on molecular terms. Looking for the missing link between biological disciplines dealing with different levels of biological organization, we suggest to return to the original intent behind the term “gene”. To this end, we propose to investigate whether a useful notion of “gene” can be constructed based on an underlying notion of function, and whether this can serve as the necessary link and embed the various distinct gene concepts of biological (sub)disciplines in a coherent theoretical framework. In reply to the Genon Theory recently put forward by Klaus Scherrer and Jürgen Jost in this journal, we shall discuss a general approach to assess a gene definition that should then be tested for its expressiveness and potential cross-disciplinary relevance

On the Efficiency of Atomic Multi-reader, Multi-writer Distributed Memory

This paper considers quorum-replicated, multi-writer, multi-reader (MWMR) implementations of surviv-able atomic registers in a distributed message-passing system with processors prone to failures. Previous implementations in such settings invariably required two rounds of communication between readers/writers and replica owners. Hence the question arises whether it is possible to have single round read and/or write operations in this setting. As a first step, we present an algorithm, called CWFR, that allows the classic two round write operations, while supporting single round read operations. Since multiple write operations may be concurrent with a read operation, this algorithm involves an iterative (local) discovery of the latest completed write operation. This algorithm precipitates the question of whether fast (single round) writes may co-exist with fast reads. We thus devise a second algorithm, called SFW, that exploits a new technique called server side ordering (SSO), which –unlike previous approaches – places partial responsibility for the ordering of write operations on the replica owners (the servers). With SSO, fast write operations are introduced for the very first time in the MWMR setting. While this is possible, we show that under certain conditions the MWMR model imposes in-herent limitations on any quorum-based fast write implementation of a safe read/write register and potentiall

Blockchains and the commons

Blockchain phenomena is similar to the last century gold rush. Blockchain technologies are publicized as being the technical solution for fully decentralizing activities that were for centuries centralized such as administration and banking. Therefore, prominent socio-economical actors all over the world are attracted and ready to invest in these technologies. Despite their large publicity, blockchains are far from being a technology ready to be used in critical economical applications and scientists multiply their effort in warning about the risks of using this technology before understanding and fully mastering it. That is, a blockchain technology evolves in a complex environment where rational and irrational behaviors are melted with faults and attacks. This position paper advocates that the theoretical foundations of blockchains should be a cross research between classical distributed systems, distributed cryptography, self-organized micro-economies, game theory and formal methods. We discuss in the following a set of open research directions interesting in this context