Recent Large Language Models (LLMs) have reported high accuracy on reasoning benchmarks. However, it is still unclear whether the observed results arise from true “reasoning” or from statistical recall of the training set. Inspired by the ladder of causation (Pearl, 2009) and its three levels (associations, interventions and counterfactuals), this paper introduces RE-IMAGINE: a framework to characterize a hierarchy of reasoning ability in LLMs, alongside an automated pipeline to generate problem variations at different levels of the hierarchy. By altering problems in an intermediate symbolic representation, RE-IMAGINE generates arbitrarily many problems that are not solvable using memorization alone. Moreover, the framework is general and can work across reasoning domains, including math, code, and logic. We demonstrate our framework on four widely-used benchmarks to evaluate several families of LLMs, and observe reductions in performance when the models are queried with problem variations. These assessments indicate a degree of reliance on statistical recall for past performance, and open the door to further research targeting skills across the reasoning hierarchy.

Memory safety violations in low-level code, written in languages like C, continues to remain one of the major sources of software vulnerabilities. One method of removing such violations by construction is to port C code to a safe C dialect. Such dialects rely on programmer-supplied annotations to guarantee safety with minimal runtime overhead. This porting, however, is a manual process that imposes significant burden on the programmer and, hence, there has been limited adoption of this technique. The task of porting not only requires inferring annotations, but may also need refactoring/rewriting of the code to make it amenable to such annotations. In this paper, we use Large Language Models (LLMs) towards addressing both these concerns. We show how to harness LLM capabilities to do complex code reasoning as well as rewriting of large codebases. We also present a novel framework for whole-program transformations that leverages lightweight static analysis to break the transformation into smaller steps that can be carried out effectively by an LLM. We implement our ideas in a tool called MSA that targets the CheckedC dialect. We evaluate MSA on several micro-benchmarks, as well as real-world code ranging up to 20K lines of code. We showcase superior performance compared to a vanilla LLM baseline, as well as demonstrate improvement over a state-of-the-art symbolic (non-LLM) technique.

We consider the problem of actively secure two-party machine-learning inference in the preprocessing model, where the parties obtain (input-independent) correlated randomness in an offline phase that they can then use to run an efficient protocol in the (input-dependent) online phase. In this setting, the state-of-the-art is the work of Escudero et al. (Crypto 2020); unfortunately, that protocol requires a large amount of correlated randomness, extensive communication, and many rounds of interaction, which leads to poor performance. In this work, we show protocols for this setting based on function secret sharing (FSS) that beat the state-of-the-art in all parameters: they use less correlated randomness and fewer rounds, and require lower communication and computation. We achieve this in part by allowing for a mix of boolean and arithmetic values in FSS-based protocols (something not done in prior work), as well as by relying on “interactive FSS;’ a generalization of FSS we introduce. To demonstrate the effectiveness of our approach we build SHARK-the first FSS-based system for actively secure inference-which outperforms the state-of-the-art by up to 2300×.

Distributed training that enables multiple parties to jointly train a model on their respective datasets is a promising approach to address the challenges of large volumes of diverse data for training modern machine learning models. However, this approach immedi- ately raises security and privacy concerns; both about each party wishing to protect its data from other parties during training and preventing leakage of private information from the model after training through various inference attacks. In this paper, we ad- dress both these concerns simultaneously by designing efficient Differentially Private, secure Multiparty Computation (DP-MPC) protocols for jointly training a model on data distributed among multiple parties. Our DP-MPC protocol in the two-party setting is 56-794× more communication-efficient and 16-182× faster than previous such protocols. Conceptually, our work simplifies and improves on previous attempts to combine techniques from secure multiparty computation and differential privacy, especially in the context of ML training.

Secure Two-party Computation (2PC) allows two parties to compute any function on their private inputs without revealing their inputs to each other. In the offline/on- line model for 2PC, correlated randomness that is independent of all inputs to the computation, is generated in a preprocessing (offline) phase and this randomness is then utilized in the online phase once the inputs to the parties become available. Most 2PC works focus on optimizing the online time as this overhead lies on the critical path. A recent paradigm for obtaining efficient 2PC protocols with low online cost is based on the cryptographic technique of function secret sharing (FSS).We build an end-to-end system Orca to accelerate the computation of FSS-based 2PC protocols with GPUs. Next, we observe that the main performance bottleneck in such accelerated protocols is in storage (due to the large amount of correlated randomness), and we design new FSS-based 2PC protocols for several key functionalities in ML which reduce storage by up to 5×. Compared to prior state-of-the-art on secure training accelerated with GPUs in the same computation model (PIRANHA, Usenix Security 2022), we show that Orca has 4% higher accuracy, 98 × lesser communication, and is 22 × faster on CIFAR-10. For secure ImageNet inference, Orca achieves sub-second latency for VGG-16 and ResNet-50 and outperforms the state-of-the-art by 8 — 103 ×.

Secure 2-party computation (2PC) enables secure inference that offers protection for both proprietary machine learning (ML) models and sensitive inputs to them. However, the existing secure inference solutions suffer from high latency and communication overheads, particularly for transformers. Function secret sharing (FSS) is a recent paradigm for obtaining efficient 2PC protocols with a preprocessing phase. We provide Sigma, the first end-to-end system for secure transformer inference based on FSS. By constructing new FSS-based protocols for complex machine learning functionalities, such as Softmax, GeLU and SiLU, and also accelerating their computation on GPUs, Sigma improves the latency of secure inference of transformers by 11 - 19x over the state-of-the-art that uses preprocessing and GPUs. We present the first secure inference of generative pre-trained transformer (GPT) models. In particular, Sigma executes Meta's Llama2 (available on HuggingFace) with 13 billion parameters in 44 seconds and GPT2 in 1.6 seconds

Running machine learning inference on tiny devices, known as TinyML, is an emerging research area. This task requires generating inference code that uses memory frugally, a task that standard ML frameworks are ill-suited for. A deployment framework for TinyML must a) be parametric in the number representation to take advantage of the emerging representations like posits, b) carefully assign high-precision to a few tensors so that most tensors can be kept in low-precision while still maintaining model accuracy, and c) avoid memory fragmentation. We describe MinUn, the first TinyML framework that holistically addresses these issues to generate efficient code for ARM microcontrollers (e.g., Arduino Uno, Due and STM32H747) that outperforms the prior TinyML frameworks.

Privacy-preserving machine learning (PPML) promises to train machine learning (ML) models by combining data spread across multiple data silos. Theoretically, secure multiparty computation (MPC) allows multiple data owners to train models on their joint data without revealing the data to each other. However, the prior implementations of this secure training using MPC have three limitations: they have only been evaluated on CNNs, and LSTMs have been ignored; fixed point approximations have affected training accuracies compared to training in floating point; and due to significant latency overheads of secure training via MPC, its relevance for practical tasks with streaming data remains unclear. The motivation of this work is to report our experience of addressing the practical problem of secure training and inference of models for urban sensing problems, e.g., traffic congestion estimation, or air pollution monitoring in large cities, where data can be contributed by rival fleet companies while balancing the privacy-accuracy trade-offs using MPC-based techniques.Our first contribution is to design a custom ML model for this task that can be efficiently trained with MPC within a desirable latency. In particular, we design a GCN-LSTM and securely train it on time-series sensor data for accurate forecasting, within 7 minutes per epoch. As our second contribution, we build an end-to-end system of private training and inference that provably matches the training accuracy of cleartext ML training. This work is the first to securely train a model with LSTM cells. Third, this trained model is kept secret-shared between the fleet companies and allows clients to make sensitive queries to this model while carefully handling potentially invalid queries. Our custom protocols allow clients to query predictions from privately trained models in milliseconds, all the while maintaining accuracy and cryptographic security.

Large pre-trained language models such as GPT-3 [10], Codex [11], and Google's language model [7] are now capable of generating code from natural language specifications of programmer intent. We view these developments with a mixture of optimism and caution. On the optimistic side, such large language models have the potential to improve productivity by providing an automated AI pair programmer for every programmer in the world. On the cautionary side, since these large language models do not understand program semantics, they offer no guarantees about quality of the suggested code. In this paper, we present an approach to augment these large language models with post-processing steps based on program analysis and synthesis techniques, that understand the syntax and semantics of programs. Further, we show that such techniques can make use of user feedback and improve with usage. We present our experiences from building and evaluating such a tool Jigsaw, targeted at synthesizing code for using Python Pandas API using multi-modal inputs. Our experience suggests that as these large language models evolve for synthesizing code from intent, Jigsaw has an important role to play in improving the accuracy of the systems.

We build a library SecFloat for secure 2-party computation (2PC) of 32-bit single-precision floating-point operations and math functions. The existing functionalities used in cryptographic works are imprecise and the precise functionalities used in standard libraries are not crypto-friendly, i.e., they use operations that are cheap on CPUs but have exorbitant cost in 2PC. SecFloat bridges this gap with its novel crypto-friendly precise functionalities. Compared to the prior cryptographic libraries, SecFloat is up to six orders of magnitude more precise and up to two orders of magnitude more efficient. Furthermore, against a precise 2PC baseline, SecFloat is three orders of magnitude more efficient. The high precision of SecFloat leads to the first accurate implementation of secure inference. All prior works on secure inference of deep neural networks rely on ad hoc float-to-fixed converters. We evaluate a model where the fixed-point approximations used in privacy-preserving machine learning completely fail and floating-point is necessary. Thus, emphasizing the need for libraries like SecFloat.

Recent breakthroughs in ML have produced new classes of models that allow ML inference to run directly on milliwatt-powered IoT devices. On one hand, existing ML-to-FPGA compilers are designed for deep neural-networks on large FPGAs. On the other hand, general-purpose HLS tools fail to exploit properties specific to ML inference, thereby resulting in suboptimal performance. We propose MAFIA, a tool to compile ML inference on small form-factor FPGAs for IoT applications. MAFIA provides native support for linear algebra operations and can express a variety of ML algorithms, including state-of-the-art models. We show that MAFIA-generated programs outperform best-performing variant of a commercial HLS compiler by 2.5 × on average.

Complex machine learning (ML) inference algorithms like recurrent neural networks (RNNs) use standard functions from math libraries like exponentiation, sigmoid, tanh, and reciprocal of square root. Although prior work on secure 2-party inference provides specialized protocols for convolutional neural networks (CNNs), existing secure implementations of these math operators rely on generic 2-party computation (2PC) protocols that suffer from high communication. We provide new specialized 2PC protocols for math functions that crucially rely on lookup-tables and mixed-bitwidths to address this performance overhead; our protocols for math functions communicate up to 423× less data than prior work. Furthermore, our math implementations are numerically precise, which ensures that the secure implementations preserve model accuracy of cleartext. We build on top of our novel protocols to build SiRnn, a library for end-to-end secure 2-party DNN inference, that provides the first secure implementations of an RNN operating on time series sensor data, an RNN operating on speech data, and a state-of-the-art ML architecture that combines CNNs and RNNs for identifying all heads present in images. Our evaluation shows that SiRnn achieves up to three orders of magnitude of performance improvement when compared to inference of these models using an existing state-of-the-art 2PC framework.

We present CrypTFlow2, a cryptographic framework for secure inference over realistic Deep Neural Networks (DNNs) using secure 2-party computation. CrypTFlow2 protocols are both correct -- i.e., their outputs are bitwise equivalent to the cleartext execution -- and efficient -- they outperform the state-of-the-art protocols in both latency and scale. At the core of CrypTFlow2, we have new 2PC protocols for secure comparison and division, designed carefully to balance round and communication complexity for secure inference tasks. Using CrypTFlow2, we present the first secure inference over ImageNet-scale DNNs like ResNet50 and DenseNet121. These DNNs are at least an order of magnitude larger than those considered in the prior work of 2-party DNN inference. Even on the benchmarks considered by prior work, CrypTFlow2 requires an order of magnitude less communication and 20x-30x less time than the state-of-the-art.

We present CrypTFlow, a first of its kind system that converts TensorFlow inference code into Secure Multi-party Computation (MPC) protocols at the push of a button. To do this, we build three components. Our first component, Athos, is an end-to-end compiler from TensorFlow to a variety of semihonest MPC protocols. The second component, Porthos, is an improved semi-honest 3-party protocol that provides significant speedups for TensorFlow like applications. Finally, to provide malicious secure MPC protocols, our third component, Aramis, is a novel technique that uses hardware with integrity guarantees to convert any semi-honest MPC protocol into an MPC protocol that provides malicious security. The malicious security of the protocols output by Aramis relies on integrity of the hardware and semi-honest security of MPC. Moreover, our system matches the inference accuracy of plaintext TensorFlow.We experimentally demonstrate the power of our system by showing the secure inference of real-world neural networks such as ResNet50 and DenseNet121 over the ImageNet dataset with running times of about 30 seconds for semi-honest security and under two minutes for malicious security. Prior work in the area of secure inference has been limited to semi-honest security of small networks over tiny datasets such as MNIST or CIFAR. Even on MNIST/CIFAR, CrypTFlow outperforms prior work.

Traditionally, IoT devices send collected sensor data to an intelligent cloud where machine learning (ML) inference happens. However, this course is rapidly changing and there is a recent trend to run ML on the edge IoT devices themselves. An intelligent edge is attractive because it saves network round trip (efficiency) and keeps user data at the source (privacy). However, the IoT devices are much more resource constrained than the cloud, which makes running ML on them challenging. Specifically, consider Arduino Uno, a commonly used board, that has 2KB of RAM and 32KB of read-only Flash memory. Although recent breakthroughs in ML have created novel recurrent neural network (RNN) models that provide good accuracy with KB-sized models, deploying them on tiny devices with such hard memory requirements has remained elusive. We provide, Shiftry, an automatic compiler from high-level floating-point ML models to fixed-point C-programs with 8-bit and 16-bit integers, which have significantly lower memory requirements. For this conversion, Shiftry uses a data-driven float-to-fixed procedure and a RAM management mechanism. These techniques enable us to provide first empirical evaluation of RNNs running on tiny edge devices. On simpler ML models that prior work could handle, Shiftry-generated code has lower latency and higher accuracy.

In syntax-guided synthesis (SyGuS), a synthesizer’s goal is to automatically generate a program belonging to a grammar of possible implementations that meets a logical specification. We investigate a common limitation across state-of-the-art SyGuS tools that perform counterexample-guided inductive synthesis (CEGIS). We empirically observe that as the expressiveness of the provided grammar increases, the performance of these tools degrades significantly. We claim that this degradation is not only due to a larger search space, but also due to overfitting. We formally define this phenomenon and prove no-free-lunch theorems for SyGuS, which reveal a fundamental tradeoff between synthesizer performance and grammar expressiveness. A standard approach to mitigate overfitting in machine learning is to run multiple learners with varying expressiveness in parallel. We demonstrate that this insight can immediately benefit existing SyGuS tools. We also propose a novel single-threaded technique called hybrid enumeration that interleaves different grammars and outperforms the winner of the 2018 SyGuS competition (Inv track), solving more problems and achieving a $$5\times $$ mean speedup.

Recent work in networked systems has shown that using aerial imagery for farm monitoring can enable precision agriculture by lowering the cost and reducing the overhead of large scale sensor deployment. However, acquiring aerial imagery requires a drone, which has high capital and operational costs, often beyond the reach of farmers in the developing world. In this paper, we present TYE (Tethered eYE), an inexpensive platform for aerial imagery. It consists of a tethered helium balloon with a custom mount that can hold a smartphone (or a camera) with a battery pack. The balloon can be carried using a tether by a person or a vehicle. We incorporate various techniques to increase the operational time of the system, and to provide actionable insights even with unstable imagery. We develop path-planning algorithms and use that to develop an interactive mobile phone application that provides the user instant feedback to guide users to efficiently traverse large areas of land. We use computer vision algorithms to stitch orthomosaics by effectively countering wind-induced motion of the camera. We have used TYE for aerial imaging of agricultural land for over a year, and envision it as a low-cost aerial imaging platform for similar applications.

Static analyses make the increasingly tenuous assumption that all source code is available for analysis; for example, large libraries often call into native code that cannot be analyzed. We propose a points-to analysis that initially makes optimistic assumptions about missing code, and then inserts runtime checks that report counterexamples to these assumptions that occur during execution. Our approach guarantees eventual soundness, which combines two guarantees: (i) the runtime checks are guaranteed to catch the first counterexample that occurs during any execution, in which case execution can be terminated to prevent harm, and (ii) only finitely many counterexamples ever occur, implying that the static analysis eventually becomes statically sound with respect to all remaining executions. We implement Optix, an eventually sound points-to analysis for Android apps, where the Android framework is missing. We show that the runtime checks added by Optix incur low overhead on real programs, and demonstrate how Optix improves a client information flow analysis for detecting Android malware.

We present EzPC, a secure two-party computation (2PC) framework that generates efficient 2PC protocols from high-level, easy-to-write programs. EzPC provides formal correctness and security guarantees while maintaining performance and scalability. Previous language frameworks, such as CBMC-GC, ObliVM, SMCL, and Wysteria, generate protocols that use either arithmetic or boolean circuits exclusively. Our compiler is the first to generate protocols that combine both arithmetic and boolean circuits for better performance. We empirically demonstrate that the performance of the protocols generated by EzPC is comparable to or better than (in some cases upto 19x) their state-of-the-art, hand-crafted implementations, while EzPC protocols also outperform their boolean circuits only counterparts by as much as 25x.

We introduce a robust semantics-driven technique for program equivalence checking. Given two functions we find a trace alignment over a set of concrete executions of both programs and construct a product program particularly amenable to checking equivalence.

Recent advances in machine learning (ML) have produced KiloByte-size models that can directly run on constrained IoT devices. This approach avoids expensive communication between IoT devices and the cloud, thereby enabling energy-efficient real-time analytics. However, ML models are expressed typically in floating-point, and IoT hardware typically does not support floating-point. Therefore, running these models on IoT devices requires simulating IEEE-754 floating-point using software, which is very inefficient.

When analyzing programs, large libraries pose significant challenges to static points-to analysis. A popular solution is to have a human analyst provide points-to specifications that summarize relevant behaviors of library code, which can substantially improve precision and handle missing code such as native code. We propose Atlas, a tool that automatically infers points-to specifications. Atlas synthesizes unit tests that exercise the library code, and then infers points-to specifications based on observations from these executions. Atlas automatically infers specifications for the Java standard library, and produces better results for a client static information flow analysis on a benchmark of 46 Android apps compared to using existing handwritten specifications.

The proliferation of Internet of Things (IoT) devices has led to the deployment of various types of sensors in the homes, offices, buildings, lawns, cities, and even in agricultural farms. Since IoT applications rely on the fidelity of data reported by the sensors, it is important to detect a faulty sensor and isolate the cause of the fault. Existing fault detection techniques demand sensor domain knowledge along with the contextual information and historical data from similar near-by sensors. However, detecting a sensor fault by analyzing just the sensor data is non-trivial since a faulty sensor reading could mimic non-faulty sensor data. This paper presents a novel primitive, which we call the Fall-curve - a sensor's voltage response when the power is turned off - that can be used to characterize sensor faults. The Fall-curve constitutes a unique signature independent of the phenomenon being monitored which can be used to identify the sensor and determine whether the sensor is correctly operating.

The proliferation of Internet of Things (IoT) devices has led to the deployment of various types of sensors in the homes, offices, buildings, lawns, cities, and even in agricultural farms. Due to the diverse nature of IoT deployments and the likelihood of sensor failures in-the-wild, a key challenge in the design of IoT systems is ensuring the integrity, accuracy, and fidelity of sensor data.

User experience in modern content discovery applications critically depends on high-quality personalized recommendations. However, building systems that provide such recommendations presents a major challenge due to a massive pool of items, a large number of users, and requirements for recommendations to be responsive to user actions and generated on demand in real-time. Here we present Pixie, a scalable graph-based real-time recommender system that we developed and deployed at Pinterest. Given a set of user-specific pins as a query, Pixie selects in real-time from billions of possible pins those that are most related to the query. To generate recommendations, we develop Pixie Random Walk algorithm that utilizes the Pinterest object graph of 3 billion nodes and 17 billion edges. Experiments show that recommendations provided by Pixie lead up to 50% higher user engagement when compared to the previous Hadoop-based production system. Furthermore, we develop a graph pruning strategy at that leads to an additional 58% improvement in recommendations. Last, we discuss system aspects of Pixie, where a single server executes 1,200 recommendation requests per second with 60 millisecond latency. Today, systems backed by Pixie contribute to more than 80% of all user engagement on Pinterest.

Industry standard implementations of math.h claim (often without formal proof) tight bounds on floating-point errors. We demonstrate a novel static analysis that proves these bounds and verifies the correctness of these implementations. Our key insight is a reduction of this verification task to a set of mathematical optimization problems that can be solved by off-the-shelf computer algebra systems. We use this analysis to prove the correctness of implementations in Intel's math library automatically. Prior to this work, these implementations could only be verified with significant manual effort.

Software fault isolation (SFI) is an important technique for the construction of secure operating systems, web browsers, and other extensible software. We demonstrate that superoptimization can dramatically improve the performance of Google Native Client, a SFI system that ships inside the Google Chrome Browser. Key to our results are new techniques for superoptimization of loops: we propose a new architecture for superoptimization tools that incorporates both a fully sound verification technique to ensure correctness and a bounded verification technique to guide the search to optimized code. In our evaluation we optimize 13 libc string functions, formally verify the correctness of the optimizations and report a median and average speedup of 25% over the libraries shipped by Google.

We present an algorithm for synthesizing a context-free grammar encoding the language of valid program inputs from a set of input examples and blackbox access to the program. Our algorithm addresses shortcomings of existing grammar inference algorithms, which both severely overgeneralize and are prohibitively slow. Our implementation, GLADE, leverages the grammar synthesized by our algorithm to fuzz test programs with structured inputs. We show that GLADE substantially increases the incremental coverage on valid inputs compared to two baseline fuzzers.

Algorithms that create and mutate graph data structures are challenging to implement correctly. However, verifying even basic properties of low-level implementations, such as referential integrity and memory safety, remains non-trivial. Furthermore, any extension to such a data structure multiplies the complexity of its implementation, while compounding the challenges in reasoning about correctness. We take a language design approach to this problem. We propose Seam, a language for expressing local edits to graph-like data structures, based on a relational data model, and such that data integrity can be verified automatically. We present a verification method that leverages an SMT solver, and prove it sound and precise (complete modulo termination of the SMT solver). We evaluate the verification capabilities of Seam empirically, and demonstrate its applicability to a variety of examples, most notably a new class of verification tasks derived from geometric remeshing operations used in scientific simulation and computer graphics. We describe our prototype implementation of a Seam compiler that generates low-level code, which can then be integrated into larger applications. We evaluate our compiler on a sample application, and demonstrate competitive execution time, compared to hand-written implementations.

This paper studies and optimizes automated program verification. Detailed reasoning about software behavior is often facilitated by program invariants that hold across all program executions. Finding program invariants is in fact an essential step in automated program verification. Automatic discovery of precise invariants, however, can be very difficult in practice. The problem can be simplified if one has access to a candidate set of assertions (or annotations) and the search for invariants is limited over the space defined by these annotations. Then, the main challenge is to automatically generate quality program annotations. We present an approach that infers program annotations automatically by leveraging the history of verifying related programs. Our algorithm extracts high-quality annotations from previous verification attempts, and then applies them for verifying new programs. We present a case study where we applied our algorithm to Microsoft’s Static Driver Verifier (SDV). SDV is an industrial-strength tool for verification of Windows device drivers that uses manually-tuned heuristics for obtaining a set of annotations. Our technique inferred program annotations comparable in performance to the existing annotations used in SDV that were devised manually by human experts over years. Additionally, the inferred annotations together with the existing ones improved the performance of SDV overall, proving correct 47% of drivers more while running 22% faster in our experiments.

A key problem in parallel programming is how data is partitioned: divided into subsets that can be operated on in parallel and, in distributed memory machines, spread across multiple address spaces.

The x86-64 ISA sits at the bottom of the software stack of most desktop and server software. Because of its importance, many software analysis and verification tools depend, either explicitly or implicitly, on correct modeling of the semantics of x86-64 instructions. However, formal semantics for the x86-64 ISA are difficult to obtain and often written manually through great effort. We describe an automatically synthesized formal semantics of the input/output behavior for a large fraction of the x86-64 Haswell ISA’s many thousands of instruction variants. The key to our results is stratified synthesis, where we use a set of instructions whose semantics are known to synthesize the semantics of additional instructions whose semantics are unknown. As the set of formally described instructions increases, the synthesis vocabulary expands, making it possible to synthesize the semantics of increasingly complex instructions. Using this technique we automatically synthesized formal semantics for 1,795 instruction variants of the x86-64 Haswell ISA. We evaluate the learned semantics against manually written semantics (where available) and find that they are formally equivalent with the exception of 50 instructions, where the manually written semantics contain an error. We further find the learned formulas to be largely as precise as manually written ones and of similar size.

Reasoning about floating-point is difficult and becomes only more so if there is an interplay between floating-point and bit-level operations. Even though real-world floating-point libraries use implementations that have such mixed computations, no systematic technique to verify the correctness of the implementations of such computations is known. In this paper, we present the first general technique for verifying the correctness of mixed binaries, which combines abstraction, analytical optimization, and testing. The technique provides a method to compute an error bound of a given implementation with respect to its mathematical specification. We apply our technique to Intel's implementations of transcendental functions and prove formal error bounds for these widely used routines.

We extend the data-driven approach to inferring preconditions for code from a set of test executions. Prior work requires a fixed set of features, atomic predicates that define the search space of possible preconditions, to be specified in advance. In contrast, we introduce a technique for on-demand feature learning, which automatically expands the search space of candidate preconditions in a targeted manner as necessary. We have instantiated our approach in a tool called PIE. In addition to making precondition inference more expressive, we show how to apply our feature-learning technique to the setting of data-driven loop invariant inference. We evaluate our approach by using PIE to infer rich preconditions for black-box OCaml library functions and using our loop-invariant inference algorithm as part of an automatic program verifier for C++ programs.

The aggressive optimization of heavily used kernels is an important problem in high-performance computing. However, both general purpose compilers and highly specialized tools such as superoptimizers often do not have sufficient static knowledge of restrictions on program inputs that could be exploited to produce the very best code. For many applications, the best possible code is conditionally correct: the optimized kernel is equal to the code that it replaces only under certain preconditions on the kernel's inputs. The main technical challenge in producing conditionally correct optimizations is in obtaining non-trivial and useful conditions and proving conditional equivalence formally in the presence of loops. We combine abstract interpretation, decision procedures, and testing to yield a verification strategy that can address both of these problems. This approach yields a superoptimizer for x86 that in our experiments produces binaries that are often multiple times faster than those produced by production compilers.

Previous efforts to formally verify code written for GPUs have focused solely on kernels written within the traditional data-parallel GPU programming model. No previous work has considered the higher performance, but more complex, warp-specialized kernels based on producer-consumer named barriers available on current hardware. In this work we present the first formal operational semantics for named barriers and define what it means for a warp-specialized kernel to be correct. We give algorithms for verifying the correctness of warp-specialized kernels and prove that they are both sound and complete for the most common class of warp-specialized programs. We also present WEFT, a verification tool for checking warp-specialized code. Using WEFT, we discover several non-trivial bugs in production warp-specialized kernels.

The aggressive optimization of floating-point computations is an important problem in high-performance computing. Unfortunately, floating-point instruction sets have complicated semantics that often force compilers to preserve programs as written. We present a method that treats floating-point optimization as a stochastic search problem. We demonstrate the ability to generate reduced precision implementations of Intel's handwritten C numeric library which are up to 6 times faster than the original code, and achieve end-to-end speedups of over 30% on a direct numeric simulation and a ray tracer by optimizing kernels that can tolerate a loss of precision while still remaining correct. Because these optimizations are mostly not amenable to formal verification using the current state of the art, we present a stochastic search technique for characterizing maximum error. The technique comes with an asymptotic guarantee and provides strong evidence of correctness.

It is often the case that increasing the precision of a program analysis leads to worse results. It is our thesis that this phenomenon is the result of fundamental limits on the ability to use precise abstract domains as the basis for inferring strong invariants of programs. We show that bias-variance tradeoffs, an idea from learning theory, can be used to explain why more precise abstractions do not necessarily lead to better results and also provides practical techniques for coping with such limitations. Learning theory captures precision using a combinatorial quantity called the VC dimension. We compute the VC dimension for different abstractions and report on its usefulness as a precision metric for program analyses. We evaluate cross validation, a technique for addressing bias-variance tradeoffs, on an industrial strength program verification tool called YOGI. The tool produced using cross validation has significantly better running time, finds new defects, and has fewer time-outs than the current production version. Finally, we make some recommendations for tackling bias-variance tradeoffs in program analysis.

We formulate the loop-free binary superoptimization task as a stochastic search problem. The competing constraints of transformation correctness and performance improvement are encoded as terms in a cost function, and a Markov Chain Monte Carlo sampler is used to rapidly explore the space of all possible programs to find one that is an optimization of a given target program. Although our method sacrifices completeness, the scope of programs we are able to consider, and the resulting quality of the programs that we produce, far exceed those of existing superoptimizers. Beginning from binaries compiled by llvm -O0 for 64-bit x86, our prototype implementation, STOKE, is able to produce programs which either match or outperform the code produced by gcc -O3, icc -O3, and in some cases, expert handwritten assembly.

We present a data driven algorithm for equivalence checking of two loops. The algorithm infers simulation relations using data from test runs. Once a candidate simulation relation has been obtained, off-the-shelf SMT solvers are used to check whether the simulation relation actually holds. The algorithm is sound: insufficient data will cause the proof to fail. We demonstrate a prototype implementation, called DDEC, of our algorithm, which is the first sound equivalence checker for loops written in x86 assembly.

Previous version of a program can be a powerful enabler for program analysis by defining new relative specifications and making the results of current program analysis more relevant. In this paper, we describe the approach of differential assertion checking (DAC) for comparing different versions of a program with respect to a set of assertions. DAC provides a natural way to write relative specifications over two programs. We introduce a novel modular approach to DAC by reducing it to safety checking of a composed program, which can be accomplished by standard program verifiers. In particular, we leverage automatic invariant generation to synthesize relative specifications for pairs of loops and procedures. We provide a preliminary evaluation of a prototype implementation within the SymDiff tool along two directions (a) soundly verifying bug fixes in the presence of loops and (b) providing a knob for suppressing alarms when checking a new version of a program.

We show how a test suite for a sequential program can be profitably used to construct a termination proof. In particular, we describe an algorithm TpT for proving termination of a program based on information derived from testing it. TpT iteratively calls two phases: (a) an infer phase, and (b) a validate phase. In the infer phase, machine learning, in particular, linear regression is used to efficiently compute a candidate loop bound for every loop in the program. These loop bounds are verified for correctness by an off-the-shelf checker. If a loop bound is invalid, then the safety checker provides a test or a counterexample that is used to generate more data which is subsequently used by the next infer phase to compute better estimates for loop bounds. On the other hand, if all loop bounds are valid, then we have a proof of termination. We also describe a simple extension to our approach that allows us to infer polynomial loop bounds automatically. We have evaluated TpT on two benchmark sets, micro-benchmarks obtained from recent literature on program termination, and Windows device drivers. Our results are promising -- on the micro-benchmarks, we show that TpT is able to prove termination on 15% more benchmarks than any previously known technique, and our evaluation on Windows device drivers demonstrates TpT's ability to analyze and scale to real world applications.

Using homomorphic encryption and secure multiparty computation, cloud servers may perform regularly structured computation on encrypted data, without access to decryption keys. However, prior approaches for programming on encrypted data involve restrictive models such as boolean circuits, or standard languages that do not guarantee secure execution of all expressible programs. We present an expressive core language for secure cloud computing, with primitive types, conditionals, standard functional features, mutable state, and a secrecy preserving form of general recursion. This language, which uses an augmented information-flow type system to prevent control-flow leakage, allows programs to be developed and tested using conventional means, then exported to a variety of secure cloud execution platforms, dramatically reducing the amount of specialized knowledge needed to write secure code. We present a Haskell-based implementation and prove that cloud implementations based on secret sharing, homomorphic encryption, or other alternatives satisfying our general definition meet precise security requirements.

In cloud computing, a client may request computation on confidential data that is sent to untrusted servers. While homomorphic encryption and secure multiparty computation provide building blocks for secure computation, software must be properly structured to preserve confidentiality. Using a general definition of secure execution platform, we propose a single Haskell-based domain-specific language for cryptographic cloud computing and prove correctness and confidentiality for two representative and distinctly different implementations of the same programming language. The secret sharing execution platform provides information-theoretic security against colluding servers. The homomorphic encryption execution platform requires only one server, but has limited efficiency, and provides secrecy against a computationally-bounded adversary. Experiments with our implementation suggest promising computational feasibility, as cryptography improves, and show how code can be developed uniformly for a variety of secure cloud platforms, without explicitly programming separate clients and servers.