We present RAND, an input-output relational abstract domain that expresses relations between values of non-recursive algebraic data types (ADTs), and numeric their scalar parts. RAND is parametrised on a user-provided domain, we lift to pairs variables projection paths. It constructed as disjunctive completion reduced product domains for relations, equalities, cases variant constructors. Using ...

We have revisited the silhouette algorithm developed by Canny, and designed its new symbolic-numeric version. The symbolic-numeric silhouette algorithm do not require the symbolic computation of the determinants of resultant matrices, and can work on oating point arithmetic. Though its combinatorial complexity remains the same, but its algebraic complexity has been improved signi cantly which i...

The Hilbert and Fourier transforms are tools used for signal analysis in the time/frequency domains. The Hilbert transform is applied to casual continuous signals. The majority of the practical signals are discrete signals and they are limited in time. It appeared therefore the need to create numeric algorithms for the Hilbert transform. Such an algorithm is a numeric operator, named the Discre...

This paper introduces a new way of accelerating the convergence of numeric CSP filtering algorithms, through the use of extrapolation methotis. Extrapolation methods are used in numerical analysis to accelerate the convergence of real number sequences. We will show how to use them for solving numeric csPs, leading to drastic improvement in efficiency.

The Formal Synthesis methodology can be considered as the application of the transformational approach to circuit synthesis by logical transformations performed in a theorem prover. Additionally to the implementation of the circuit, the proof that the result is a correct implementation of a given specification is obtained automatically. In this paper, a higher-order formalisation for the arithm...

Multiparadigm programming allows the programmer to write the implementation of a system in a number of different paradigms. We describe our approach to multiparadigm programming based on modeling programming paradigms as object classes. In particular, objects can be used to encapsulate program modules, and classes to encapsulate their respective paradigms. The paradigm class hierarchy can then ...

In many database applications, ranking queries may reference both text and numeric attributes, where the ranking functions are based on both semantic distances/similarities for text attributes and numeric distances for numeric attributes. In this paper, we propose a new method for evaluating such type of ranking queries over a relational database. By statistics and training, this method builds ...

The paper addresses the problem of plan repair for tasks involving mandatory constraints on consumable and continuous resources, modeled as numeric fluents. The approach starts by proposing a new notion of numeric macro actions allowing to handle as an extension to the classical macro action formulation conditions and operations not only on the propositional fragment, but also on the numeric on...