Symbolic Robustness Analysis

Majumdar, Rupak; Saha, Indranil

doi:10.1109/rtss.2009.17

Cited by 53 publications

(53 citation statements)

References 10 publications

(8 reference statements)

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“…However, sampling cannot be applied in our context as representation error bounds are too small to be representable without using higher precision. Static analysis has also been proposed to prove a program is continuous [6,17,26] or robust [7,34] in the presence of input errors.…”

Section: Related Workmentioning

confidence: 99%

On-the-fly detection of instability problems in floating-point program execution

BaoTao

ZhangXiangyu

2013

SIGPLAN Not.

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The machine representation of floating point values has limited precision such that errors may be introduced during execution. These errors may get propagated and magnified by the following operations, leading to instability problems, e.g., control flow path may be undesirably altered and faulty output may be emitted. In this paper, we develop an onthe-fly efficient monitoring technique that can predict if an execution is stable. The technique does not explicitly compute errors as doing so incurs high overhead. Instead, it detects possible places where an error becomes substantially inflated regarding the corresponding value, and then tags the value with one bit to denote that it has an inflated error. It then tracks inflation bit propagation, taking care of operations that may cut off such propagation. It reports instability if any inflation bit reaches a critical execution point, such as a predicate, where the inflated error may induce substantial execution difference, such as different execution paths. Our experiment shows that with appropriate thresholds, the technique can correctly detect that over 99.999996% of the inputs of all the programs we studied are stable while a traditional technique relying solely on inflation detection mistakenly classifies majority of the inputs as unstable for some of the programs. Compared to the state of the art technique that is based on high precision computation and causes several hundred times slowdown, our technique only causes 7.91 times slowdown on average and can report all the true unstable executions with the appropriate thresholds.

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Section: Related Workmentioning

confidence: 99%

On-the-fly detection of instability problems in floating-point program execution

BaoTao

ZhangXiangyu

2013

SIGPLAN Not.

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“…In prior work [15], [4][5][6] on continuity and robustness analysis, the focus is on checking if the function computed by a program has desirable properties such as Lipschitz continuity. While these papers reason about programs that manipulate numbers, we focus on robustness analysis of programs manipulating strings.…”

Section: Related Workmentioning

confidence: 99%

“…One way to ensure that a transducer behaves reliably on uncertain inputs is to show that it is robust, as formalized in [15,4,6]. Informally, robustness means that small perturbations to the transducer's inputs can only lead to small changes in the corresponding outputs.…”

Section: Introductionmentioning

confidence: 99%

Robustness Analysis of String Transducers

Samanta

Deshmukh

Chaudhuri

2013

Automated Technology for Verification and Analysis

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Abstract. Many important functions over strings can be represented as finite-state string transducers. In this paper, we present an automatatheoretic technique for algorithmically verifying that such a function is robust to uncertainty. A function encoded as a transducer is defined to be robust if for each small (i.e., bounded) change to any input string, the change in the transducer's output is proportional to the change in the input. Changes to input and output strings are quantified using weighted generalizations of the Levenshtein and Manhattan distances over strings. Our main technical contribution is a set of decision procedures based on reducing the problem of robustness verification of a transducer to the problem of checking the emptiness of a reversal-bounded counter machine. The decision procedures under the generalized Manhattan and Levenshtein distance metrics are in Pspace and Expspace, respectively. For transducers that are Mealy machines, the decision procedures under these metrics are in Nlogspace and Pspace, respectively.

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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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Symbolic Robustness Analysis

Cited by 53 publications

References 10 publications

On-the-fly detection of instability problems in floating-point program execution

On-the-fly detection of instability problems in floating-point program execution

Robustness Analysis of String Transducers

Randomized accuracy-aware program transformations for efficient approximate computations

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