9,166 research outputs found
Formalization and Validation of Safety-Critical Requirements
The validation of requirements is a fundamental step in the development
process of safety-critical systems. In safety critical applications such as
aerospace, avionics and railways, the use of formal methods is of paramount
importance both for requirements and for design validation. Nevertheless, while
for the verification of the design, many formal techniques have been conceived
and applied, the research on formal methods for requirements validation is not
yet mature. The main obstacles are that, on the one hand, the correctness of
requirements is not formally defined; on the other hand that the formalization
and the validation of the requirements usually demands a strong involvement of
domain experts. We report on a methodology and a series of techniques that we
developed for the formalization and validation of high-level requirements for
safety-critical applications. The main ingredients are a very expressive formal
language and automatic satisfiability procedures. The language combines
first-order, temporal, and hybrid logic. The satisfiability procedures are
based on model checking and satisfiability modulo theory. We applied this
technology within an industrial project to the validation of railways
requirements
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
Formalized linear algebra over Elementary Divisor Rings in Coq
This paper presents a Coq formalization of linear algebra over elementary
divisor rings, that is, rings where every matrix is equivalent to a matrix in
Smith normal form. The main results are the formalization that these rings
support essential operations of linear algebra, the classification theorem of
finitely presented modules over such rings and the uniqueness of the Smith
normal form up to multiplication by units. We present formally verified
algorithms computing this normal form on a variety of coefficient structures
including Euclidean domains and constructive principal ideal domains. We also
study different ways to extend B\'ezout domains in order to be able to compute
the Smith normal form of matrices. The extensions we consider are: adequacy
(i.e. the existence of a gdco operation), Krull dimension and
well-founded strict divisibility
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
CASP Solutions for Planning in Hybrid Domains
CASP is an extension of ASP that allows for numerical constraints to be added
in the rules. PDDL+ is an extension of the PDDL standard language of automated
planning for modeling mixed discrete-continuous dynamics.
In this paper, we present CASP solutions for dealing with PDDL+ problems,
i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP
CASP solver in order to solve CASP programs arising from PDDL+ domains. An
experimental analysis, performed on well-known linear and non-linear variants
of PDDL+ domains, involving various configurations of the EZCSP solver, other
CASP solvers, and PDDL+ planners, shows the viability of our solution.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
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