62,794 research outputs found
Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program
Computer programs may go wrong due to exceptional behaviors, out-of-bound
array accesses, or simply coding errors. Thus, they cannot be blindly trusted.
Scientific computing programs make no exception in that respect, and even bring
specific accuracy issues due to their massive use of floating-point
computations. Yet, it is uncommon to guarantee their correctness. Indeed, we
had to extend existing methods and tools for proving the correct behavior of
programs to verify an existing numerical analysis program. This C program
implements the second-order centered finite difference explicit scheme for
solving the 1D wave equation. In fact, we have gone much further as we have
mechanically verified the convergence of the numerical scheme in order to get a
complete formal proof covering all aspects from partial differential equations
to actual numerical results. To the best of our knowledge, this is the first
time such a comprehensive proof is achieved.Comment: N° RR-8197 (2012). arXiv admin note: text overlap with
arXiv:1112.179
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
Towards Practical Graph-Based Verification for an Object-Oriented Concurrency Model
To harness the power of multi-core and distributed platforms, and to make the
development of concurrent software more accessible to software engineers,
different object-oriented concurrency models such as SCOOP have been proposed.
Despite the practical importance of analysing SCOOP programs, there are
currently no general verification approaches that operate directly on program
code without additional annotations. One reason for this is the multitude of
partially conflicting semantic formalisations for SCOOP (either in theory or
by-implementation). Here, we propose a simple graph transformation system (GTS)
based run-time semantics for SCOOP that grasps the most common features of all
known semantics of the language. This run-time model is implemented in the
state-of-the-art GTS tool GROOVE, which allows us to simulate, analyse, and
verify a subset of SCOOP programs with respect to deadlocks and other
behavioural properties. Besides proposing the first approach to verify SCOOP
programs by automatic translation to GTS, we also highlight our experiences of
applying GTS (and especially GROOVE) for specifying semantics in the form of a
run-time model, which should be transferable to GTS models for other concurrent
languages and libraries.Comment: In Proceedings GaM 2015, arXiv:1504.0244
Formal Proofs for Nonlinear Optimization
We present a formally verified global optimization framework. Given a
semialgebraic or transcendental function and a compact semialgebraic domain
, we use the nonlinear maxplus template approximation algorithm to provide a
certified lower bound of over . This method allows to bound in a modular
way some of the constituents of by suprema of quadratic forms with a well
chosen curvature. Thus, we reduce the initial goal to a hierarchy of
semialgebraic optimization problems, solved by sums of squares relaxations. Our
implementation tool interleaves semialgebraic approximations with sums of
squares witnesses to form certificates. It is interfaced with Coq and thus
benefits from the trusted arithmetic available inside the proof assistant. This
feature is used to produce, from the certificates, both valid underestimators
and lower bounds for each approximated constituent. The application range for
such a tool is widespread; for instance Hales' proof of Kepler's conjecture
yields thousands of multivariate transcendental inequalities. We illustrate the
performance of our formal framework on some of these inequalities as well as on
examples from the global optimization literature.Comment: 24 pages, 2 figures, 3 table
Abstract Interpretation-based verification/certification in the ciaoPP system
CiaoPP is the abstract interpretation-based preprocessor of
the Ciao multi-paradigm (Constraint) Logic Programming system. It uses modular, incremental abstract interpretation as a fundamental tool to obtain information about programs. In CiaoPP, the semantic approximations thus produced have been applied to perform high- and low-level optimizations during program compilation, including transformations such as mĂşltiple abstract specialization, parallelization, partial evaluation, resource usage control, and program verification. More recently, novel and promising applications of such semantic approximations are
being applied in the more general context of program development such as program verification. In this work, we describe our extensiĂłn of the system to incorpĂłrate Abstraction-Carrying Code (ACC), a novel approach to mobile code safety. ACC follows the standard strategy of associating safety certificates to programs, originally proposed in Proof Carrying- Code. A distinguishing feature of ACC is that we use an abstraction (or abstract model) of the program computed by standard static analyzers as a certifĂcate. The validity of the abstraction on the consumer side is checked in a single-pass by a very efficient and specialized abstractinterpreter. We have implemented and benchmarked ACC within CiaoPP. The experimental results show that the checking phase is indeed faster than the proof generation phase, and that the sizes of certificates are reasonable. Moreover, the preprocessor is based on compile-time (and run-time) tools for the certification of CLP programs with resource consumption assurances
Effectively Engaging Diasporas Under the New Canadian Department of Foreign Affairs, Trade and Development
With the amalgamation of the Canadian International Development Agency (CIDA) and the Department of Foreign Affairs and International Trade (DFAIT) into a new Department of Foreign Affairs, Trade and Development (DFATD), new opportunities will emerge for a coherent approach to diaspora engagement initiatives that combine the existing policy directions under a single umbrella. DFATD should work with diasporas in Canada to facilitate and improve engagement with the sending regions. This engagement can occur through current programs, as well as the creation of a new pilot project requiring cooperation between the different policy approaches. Engagement should vary according to the different levels of formal government diasporic engagement of the sending countries, as countries with weak government engagement will require policy approaches distinct from countries with strong government engagement
Structural abstract interpretation, A formal study using Coq
interpreters are tools to compute approximations for behaviors of a program.
These approximations can then be used for optimisation or for error detection.
In this paper, we show how to describe an abstract interpreter using the
type-theory based theorem prover Coq, using inductive types for syntax and
structural recursive programming for the abstract interpreter's kernel. The
abstract interpreter can then be proved correct with respect to a Hoare logic
for the programming language
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