Proving acceptability properties of relaxed nondeterministic approximate programs

Approximate program transformations such as skipping tasks [29, 30], loop perforation [21, 22, 35], reduction sampling [38], multiple selectable implementations [3, 4, 16, 38], dynamic knobs [16], synchronization elimination [20, 32], approximate function memoization [11],and approximate data types [34] produce programs that can execute at a variety of points in an underlying performance versus accuracy tradeoff space. These transformed programs have the ability to trade accuracy of their results for increased performance by dynamically and nondeterministically modifying variables that control their execution. We call such transformed programs relaxed programs because they have been extended with additional nondeterminism to relax their semantics and enable greater flexibility in their execution. We present language constructs for developing and specifying relaxed programs. We also present proof rules for reasoning about properties [28] which the program must satisfy to be acceptable. Our proof rules work with two kinds of acceptability properties: acceptability properties [28], which characterize desired relationships between the values of variables in the original and relaxed programs, and unary acceptability properties, which involve values only from a single (original or relaxed) program. The proof rules support a staged reasoning approach in which the majority of the reasoning effort works with the original program. Exploiting the common structure that the original and relaxed programs share, relational reasoning transfers reasoning effort from the original program to prove properties of the relaxed program. We have formalized the dynamic semantics of our target programming language and the proof rules in Coq and verified that the proof rules are sound with respect to the dynamic semantics. Our Coq implementation enables developers to obtain fully machine-checked verifications of their relaxed programs.National Science Foundation (U.S.). (Grant number CCF-0811397)National Science Foundation (U.S.). (Grant number CCF-0905244)National Science Foundation (U.S.). (Grant number CCF-1036241)National Science Foundation (U.S.). (Grant number IIS-0835652)United States. Defense Advanced Research Projects Agency (Grant number FA8650-11-C-7192)United States. Defense Advanced Research Projects Agency (Grant number FA8750-12-2-0110)United States. Dept. of Energy. (Grant Number DE-SC0005288

Synthesis of Randomized Accuracy-Aware Map-Fold Programs

We present Syndy, a technique for automatically synthesizing randomized map/fold computations that trade accuracy for performance. Given a specification of a fully accurate computation, Syndy automatically synthesizes approximate implementations of map and fold tasks, explores the approximate computation space that these approximations induce, and derives an accuracy versus performance tradeoff curve that characterizes the explored space. Each point on the curve corresponds to an approximate randomized program configuration that realizes the probabilistic error and time bounds associated with that point

Data-Oriented Characterization of Application-Level Energy Optimization

Abstract. Empowering application programmers to make energy-aware decisions is a critical dimension of energy optimization for computer systems. In this paper, we study the energy impact of alternative data management choices by programmers, such as data access patterns, data precision choices, and data organization. Second, we attempt to build a bridge between application-level energy management and hardware-level energy management, by elucidating how various application-level data management features respond to Dynamic Voltage and Frequency Scal-ing (DVFS). Finally, we apply our findings to real-world applications, demonstrating their potential for guiding application-level energy opti-mization. The empirical study is particularly relevant in the Big Data era, where data-intensive applications are large energy consumers, and their energy efficiency is strongly correlated to how data are maintained and handled in programs

Quantitative Robustness Analysis of Quantum Programs (Extended Version)

Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called $\epsilon$-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.Comment: 34 pages, LaTeX; v2: fixed typo

Master of Science

thesisTo minimize resource consumption and maximize performance, computer architecture research has been investigating approaches that may compute inaccurate solutions. Such hardware inaccuracies may induce a wide variety of program behaviors which are not obs