Systematic testing for control applications

Majumdar, Rupak; Saha, Indranil; Wang, Zilong

doi:10.1109/memcod.2010.5558629

Cited by 17 publications

(10 citation statements)

References 33 publications

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“…Majumdar et al extended the Splat concolic testing engine to support floating-point and nonlinear constraints, then tackled the problems of path coverage, range and robustness analysis [30]. Lakhotia et al empirically evaluated two search-based techniques for solving numerical constraints -alternating variable method and evolution strategies [28].…”

Section: Related Workmentioning

confidence: 99%

Automatic detection of floating-point exceptions

Barr

et al. 2013

SIGPLAN Not.

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It is well-known that floating-point exceptions can be disastrous and writing exception-free numerical programs is very difficult. Thus, it is important to automatically detect such errors. In this paper, we present Ariadne, a practical symbolic execution system specifically designed and implemented for detecting floating-point exceptions. Ariadne systematically transforms a numerical program to explicitly check each exception triggering condition. Ariadne symbolically executes the transformed program using real arithmetic to find candidate real-valued inputs that can reach and trigger an exception. Ariadne converts each candidate input into a floating-point number, then tests it against the original program. In general, approximating floating-point arithmetic with real arithmetic can change paths from feasible to infeasible and vice versa. The key insight of this work is that, for the problem of detecting floating-point exceptions, this approximation works well in practice because, if one input reaches an exception, many are likely to, and at least one of them will do so over both floating-point and real arithmetic. To realize Ariadne, we also devised a novel, practical linearization technique to solve nonlinear constraints. We extensively evaluated Ariadne over 467 scalar functions in the widely used GNU Scientific Library (GSL). Our results show that Ariadne is practical and identifies a large number of real runtime exceptions in GSL. The GSL developers confirmed our preliminary findings and look forward to Ariadne's public release, which we plan to do in the near future.

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Section: Related Workmentioning

confidence: 99%

Automatic detection of floating-point exceptions

Barr

et al. 2013

SIGPLAN Not.

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“…[40] use concolic execution to find inputs which, given maximum deviations on inputs, maximize the deviation on the outputs. These two works however, use a testing approach and cannot provide sound guarantees.…”

Section: Related Workmentioning

confidence: 99%

Sound compilation of reals

Darulová

Kunčak

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

114

110

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Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and specification language that explicitly includes different types of uncertainties. We then present a compilation algorithm that generates a finite-precision implementation that is guaranteed to meet the desired precision with respect to real numbers. Our compilation performs a number of verification steps for different candidate precisions. It generates verification conditions that treat all sources of uncertainties in a unified way and encode reasoning about finiteprecision roundoff errors into reasoning about real numbers. Such verification conditions can be used as a standardized format for verifying the precision and the correctness of numerical programs. Due to their non-linear nature, precise reasoning about these verification conditions remains difficult and cannot be handled using state-of-the art SMT solvers alone. We therefore propose a new procedure that combines exact SMT solving over reals with approximate and sound affine and interval arithmetic. We show that this approach overcomes scalability limitations of SMT solvers while providing improved precision over affine and interval arithmetic. Our implementation gives promising results on several numerical models, including dynamical systems, transcendental functions, and controller implementations.

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“…Researchers have developed techniques to identify continuous or Lipschitz-continuous programs [5,6,18,19,26]. Identified applications include differential privacy [5,6,26] and robust functions for embedded systems [6,18,19].…”

Section: Related Workmentioning

confidence: 99%

Randomized accuracy-aware program transformations for efficient approximate computations

et al. 2012

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Despite the fact that approximate computations have come to dominate many areas of computer science, the field of program transformations has focused almost exclusively on traditional semanticspreserving transformations that do not attempt to exploit the opportunity, available in many computations, to acceptably trade off accuracy for benefits such as increased performance and reduced resource consumption.We present a model of computation for approximate computations and an algorithm for optimizing these computations. The algorithm works with two classes of transformations: substitution transformations (which select one of a number of available implementations for a given function, with each implementation offering a different combination of accuracy and resource consumption) and sampling transformations (which randomly discard some of the inputs to a given reduction). The algorithm produces a (1 + ε) randomized approximation to the optimal randomized computation (which minimizes resource consumption subject to a probabilistic accuracy specification in the form of a maximum expected error or maximum error variance).

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Systematic testing for control applications

Cited by 17 publications

References 33 publications

Automatic detection of floating-point exceptions

Automatic detection of floating-point exceptions

Sound compilation of reals

Randomized accuracy-aware program transformations for efficient approximate computations

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