Synthesizing Functional Reactive Programs

Functional Reactive Programming (FRP) is a paradigm that has simplified the construction of reactive programs. There are many libraries that implement incarnations of FRP, using abstractions such as Applicative, Monads, and Arrows. However, finding a good control flow, that correctly manages state and switches behaviors at the right times, still poses a major challenge to developers. An attractive alternative is specifying the behavior instead of programming it, as made possible by the recently developed logic: Temporal Stream Logic (TSL). However, it has not been explored so far how Control Flow Models (CFMs), as synthesized from TSL specifications, can be turned into executable code that is compatible with libraries building on FRP. We bridge this gap, by showing that CFMs are indeed a suitable formalism to be turned into Applicative, Monadic, and Arrowized FRP. We demonstrate the effectiveness of our translations on a real-world kitchen timer application, which we translate to a desktop application using the Arrowized FRP library Yampa, a web application using the Monadic threepenny-gui library, and to hardware using the Applicative hardware description language ClaSH.Comment: arXiv admin note: text overlap with arXiv:1712.0024

Generalized Paxos Made Byzantine (and Less Complex)

One of the most recent members of the Paxos family of protocols is Generalized Paxos. This variant of Paxos has the characteristic that it departs from the original specification of consensus, allowing for a weaker safety condition where different processes can have a different views on a sequence being agreed upon. However, much like the original Paxos counterpart, Generalized Paxos does not have a simple implementation. Furthermore, with the recent practical adoption of Byzantine fault tolerant protocols, it is timely and important to understand how Generalized Paxos can be implemented in the Byzantine model. In this paper, we make two main contributions. First, we provide a description of Generalized Paxos that is easier to understand, based on a simpler specification and the pseudocode for a solution that can be readily implemented. Second, we extend the protocol to the Byzantine fault model

On Thin Air Reads: Towards an Event Structures Model of Relaxed Memory

To model relaxed memory, we propose confusion-free event structures over an alphabet with a justification relation. Executions are modeled by justified configurations, where every read event has a justifying write event. Justification alone is too weak a criterion, since it allows cycles of the kind that result in so-called thin-air reads. Acyclic justification forbids such cycles, but also invalidates event reorderings that result from compiler optimizations and dynamic instruction scheduling. We propose the notion of well-justification, based on a game-like model, which strikes a middle ground. We show that well-justified configurations satisfy the DRF theorem: in any data-race free program, all well-justified configurations are sequentially consistent. We also show that rely-guarantee reasoning is sound for well-justified configurations, but not for justified configurations. For example, well-justified configurations are type-safe. Well-justification allows many, but not all reorderings performed by relaxed memory. In particular, it fails to validate the commutation of independent reads. We discuss variations that may address these shortcomings

MDCC: Multi-Data Center Consistency

Replicating data across multiple data centers not only allows moving the data closer to the user and, thus, reduces latency for applications, but also increases the availability in the event of a data center failure. Therefore, it is not surprising that companies like Google, Yahoo, and Netflix already replicate user data across geographically different regions. However, replication across data centers is expensive. Inter-data center network delays are in the hundreds of milliseconds and vary significantly. Synchronous wide-area replication is therefore considered to be unfeasible with strong consistency and current solutions either settle for asynchronous replication which implies the risk of losing data in the event of failures, restrict consistency to small partitions, or give up consistency entirely. With MDCC (Multi-Data Center Consistency), we describe the first optimistic commit protocol, that does not require a master or partitioning, and is strongly consistent at a cost similar to eventually consistent protocols. MDCC can commit transactions in a single round-trip across data centers in the normal operational case. We further propose a new programming model which empowers the application developer to handle longer and unpredictable latencies caused by inter-data center communication. Our evaluation using the TPC-W benchmark with MDCC deployed across 5 geographically diverse data centers shows that MDCC is able to achieve throughput and latency similar to eventually consistent quorum protocols and that MDCC is able to sustain a data center outage without a significant impact on response times while guaranteeing strong consistency

Polly's Polyhedral Scheduling in the Presence of Reductions

The polyhedral model provides a powerful mathematical abstraction to enable effective optimization of loop nests with respect to a given optimization goal, e.g., exploiting parallelism. Unexploited reduction properties are a frequent reason for polyhedral optimizers to assume parallelism prohibiting dependences. To our knowledge, no polyhedral loop optimizer available in any production compiler provides support for reductions. In this paper, we show that leveraging the parallelism of reductions can lead to a significant performance increase. We give a precise, dependence based, definition of reductions and discuss ways to extend polyhedral optimization to exploit the associativity and commutativity of reduction computations. We have implemented a reduction-enabled scheduling approach in the Polly polyhedral optimizer and evaluate it on the standard Polybench 3.2 benchmark suite. We were able to detect and model all 52 arithmetic reductions and achieve speedups up to 2.21$\times$ on a quad core machine by exploiting the multidimensional reduction in the BiCG benchmark.Comment: Presented at the IMPACT15 worksho

Tropical Limits of Probability Spaces, Part I: The Intrinsic Kolmogorov-Sinai Distance and the Asymptotic Equipartition Property for Configurations

The entropy of a finite probability space $X$ measures the observable cardinality of large independent products $X^{\otimes n}$ of the probability space. If two probability spaces $X$ and $Y$ have the same entropy, there is an almost measure-preserving bijection between large parts of $X^{\otimes n}$ and $Y^{\otimes n}$. In this way, $X$ and $Y$ are asymptotically equivalent. It turns out to be challenging to generalize this notion of asymptotic equivalence to configurations of probability spaces, which are collections of probability spaces with measure-preserving maps between some of them. In this article we introduce the intrinsic Kolmogorov-Sinai distance on the space of configurations of probability spaces. Concentrating on the large-scale geometry we pass to the asymptotic Kolmogorov-Sinai distance. It induces an asymptotic equivalence relation on sequences of configurations of probability spaces. We will call the equivalence classes \emph{tropical probability spaces}. In this context we prove an Asymptotic Equipartition Property for configurations. It states that tropical configurations can always be approximated by homogeneous configurations. In addition, we show that the solutions to certain Information-Optimization problems are Lipschitz-con\-tinuous with respect to the asymptotic Kolmogorov-Sinai distance. It follows from these two statements that in order to solve an Information-Optimization problem, it suffices to consider homogeneous configurations. Finally, we show that spaces of trajectories of length $n$ of certain stochastic processes, in particular stationary Markov chains, have a tropical limit.Comment: Comment to version 2: Fixed typos, a calculation mistake in Lemma 5.1 and its consequences in Proposition 5.2 and Theorem 6.

Theoretical framework for quantum networks

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination, estimation, and tomography. Our framework is based on the concepts of quantum comb-which describes all transformations achievable by a given quantum network-and link product-the operation of connecting two quantum networks. Quantum networks are treated both from a constructive point of view-based on connections of elementary circuits-and from an axiomatic one-based on a hierarchy of admissible quantum maps. In the axiomatic context a fundamental property is shown, which we call universality of quantum memory channels: any admissible transformation of quantum networks can be realized by a suitable sequence of memory channels. The open problem whether this property fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.Comment: 23 pages, revtex