Walid Belkhir

Fresh-Variable Automata: Application to Service Composition

We introduce fresh-variable automata, a natural extension of finite-state automata over infinite alphabet. In this model the transitions are labeled with constants or variables that can be refreshed in some specified states. We prove several closure properties for this class of automata and study their decision problems. We show the applicability of our model in modeling Web services handling data from an infinite domain. We introduce a notion of simulation that enables us to reduce the Web service composition problem to the construction of a simulation of a target service by the asynchronous product of existing services, and prove that this construction is computable.

Computer-aided multiscale model derivation for MEMS arrays

We are currently developing software dedicated to multiscale and multiphysics modeling of arrays of micro and nanosystems. Unlike traditional software that is based on models built once and for all, here this is the software that constructs models. It is based on the mathematical Two-Scale Transform, a technique for asymptotic methods, together with formal specification and verification techniques in computer science, combining formal transformations and term rewriting and type theory. We aim at taking into account a wide range of geometries combining thin structures, periodic structures with the possibility of multiple nested scales and any combination of these features. In this paper we present the principle of our methods and our first results.

Lazy AC-Pattern Matching for Rewriting

We define a lazy pattern-matching mechanism modulo associativity and commutativity. The solutions of a pattern-matching problem are stored in a lazy list composed of a first substitution at the head and a non-evaluated object that encodes the remaining computations. We integrate the lazy AC-matching in a strategy language: rewriting rule and strategy application produce a lazy list of terms.