Related papers: Synthesizing Backward Error Bounds, Backward

Backward error analysis offers a method for assessing the quality of numerical programs in the presence of floating-point rounding errors. However, techniques from the numerical analysis literature for quantifying backward error require…

Backward error (BE) analysis emerges as a powerful tool for assessing the backward stability and strong backward stability of numerical algorithms. In this paper, we explore structured BEs for a class of double saddle point problems…

Automated Synthesis Planning has recently re-emerged as a research area at the intersection of chemistry and machine learning. Despite the appearance of steady progress, we argue that imperfect benchmarks and inconsistent comparisons mask…

The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…

We explore and formalize the task of synthesizing programs over noisy data, i.e., data that may contain corrupted input-output examples. By formalizing the concept of a Noise Source, an Input Source, and a prior distribution over programs,…

We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…

This dissertation explores the design and implementation of programming languages that represent rounding error analysis through typing. In the first part of this dissertation, we demonstrate that it is possible to design languages for…

It has been the standard teaching of today that backward stability analysis is taught as absolute, just as in Newtonian physics time is taught absolute time. We will prove it is not true in general. It depends on algorithms. We will prove…

We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps…

Program synthesis is challenging largely because of the difficulty of search in a large space of programs. Human programmers routinely tackle the task of writing complex programs by writing sub-programs and then analyzing their intermediate…

The use of deep learning techniques has achieved significant progress for program synthesis from input-output examples. However, when the program semantics become more complex, it still remains a challenge to synthesize programs that are…

Software implementations of controllers for physical systems are at the core of many embedded systems. The design of controllers uses the theory of dynamical systems to construct a mathematical control law that ensures that the controlled…

Test instability in a floating-point program occurs when the control flow of the program diverges from its ideal execution assuming real arithmetic. This phenomenon is caused by the presence of round-off errors that affect the evaluation of…

Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…

Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…

With the surge of multi- and manycores, much research has focused on algorithms for mapping and scheduling on these complex platforms. Large classes of these algorithms face scalability problems. This is why diverse methods are commonly…

Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into…

State-of-the-art static analysis tools for verifying finite-precision code compute worst-case absolute error bounds on numerical errors. These are, however, often not a good estimate of accuracy as they do not take into account the…

Retrosynthesis is the task of planning a series of chemical reactions to create a desired molecule from simpler, buyable molecules. While previous works have proposed algorithms to find optimal solutions for a range of metrics (e.g.…

Provably correct software is one of the key challenges of our software-driven society. Program synthesis -- the task of constructing a program satisfying a given specification -- is one strategy for achieving this. The result of this task…