13,110 research outputs found
A Static Analyzer for Large Safety-Critical Software
We show that abstract interpretation-based static program analysis can be
made efficient and precise enough to formally verify a class of properties for
a family of large programs with few or no false alarms. This is achieved by
refinement of a general purpose static analyzer and later adaptation to
particular programs of the family by the end-user through parametrization. This
is applied to the proof of soundness of data manipulation operations at the
machine level for periodic synchronous safety critical embedded software. The
main novelties are the design principle of static analyzers by refinement and
adaptation through parametrization, the symbolic manipulation of expressions to
improve the precision of abstract transfer functions, the octagon, ellipsoid,
and decision tree abstract domains, all with sound handling of rounding errors
in floating point computations, widening strategies (with thresholds, delayed)
and the automatic determination of the parameters (parametrized packing)
Estimating the maximum rise in temperature according to climate models using abstract interpretation
Current climate models are complex computer programs that are typically iterated time-step by time-step to predict the next set of values of the climate-related variables. Since these iterative methods are necessarily computed only for a fixed number of iterations, they are unable to answer the natural question whether there is a limit to the rise of global temperature. In order to answer that question we propose to combine climate models with software verification techniques that can find invariant conditions for the set of program variables. In particular, we apply the constraint database approach to software verification to find that the rise in global temperature is bounded according to the common Java Climate Model that implements the Wigely/Raper Upwelling-Diffusion Energy Balance Model climate model
The Parma Polyhedra Library: Toward a Complete Set of Numerical Abstractions for the Analysis and Verification of Hardware and Software Systems
Since its inception as a student project in 2001, initially just for the
handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library
has been continuously improved and extended by joining scrupulous research on
the theoretical foundations of (possibly non-convex) numerical abstractions to
a total adherence to the best available practices in software development. Even
though it is still not fully mature and functionally complete, the Parma
Polyhedra Library already offers a combination of functionality, reliability,
usability and performance that is not matched by similar, freely available
libraries. In this paper, we present the main features of the current version
of the library, emphasizing those that distinguish it from other similar
libraries and those that are important for applications in the field of
analysis and verification of hardware and software systems.Comment: 38 pages, 2 figures, 3 listings, 3 table
Certified Roundoff Error Bounds Using Semidefinite Programming.
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs or custom hardware implementation. This problem becomes challenging when the program does not employ solely linear operations as non-linearities are inherent to many interesting computational problems in real-world applications. Existing solutions to reasoning are limited in the presence of nonlinear correlations between variables, leading to either imprecise bounds or high analysis time. Furthermore, while it is easy to implement a straightforward method such as interval arithmetic, sophisticated techniques are less straightforward to implement in a formal setting. Thus there is a need for methods which output certificates that can be formally validated inside a proof assistant. We present a framework to provide upper bounds on absolute roundoff errors. This framework is based on optimization techniques employing semidefinite programming and sums of squares certificates, which can be formally checked inside the Coq theorem prover. Our tool covers a wide range of nonlinear programs, including polynomials and transcendental operations as well as conditional statements. We illustrate the efficiency and precision of this tool on non-trivial programs coming from biology, optimization and space control. Our tool produces more precise error bounds for 37 percent of all programs and yields better performance in 73 percent of all programs
SWATI: Synthesizing Wordlengths Automatically Using Testing and Induction
In this paper, we present an automated technique SWATI: Synthesizing
Wordlengths Automatically Using Testing and Induction, which uses a combination
of Nelder-Mead optimization based testing, and induction from examples to
automatically synthesize optimal fixedpoint implementation of numerical
routines. The design of numerical software is commonly done using
floating-point arithmetic in design-environments such as Matlab. However, these
designs are often implemented using fixed-point arithmetic for speed and
efficiency reasons especially in embedded systems. The fixed-point
implementation reduces implementation cost, provides better performance, and
reduces power consumption. The conversion from floating-point designs to
fixed-point code is subject to two opposing constraints: (i) the word-width of
fixed-point types must be minimized, and (ii) the outputs of the fixed-point
program must be accurate. In this paper, we propose a new solution to this
problem. Our technique takes the floating-point program, specified accuracy and
an implementation cost model and provides the fixed-point program with
specified accuracy and optimal implementation cost. We demonstrate the
effectiveness of our approach on a set of examples from the domain of automated
control, robotics and digital signal processing
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