We propose a common rigorous foundation to the classical collision theory and that of the classical activated complex. Based on the notion of activated complex, this foundation relies on a stochastic approach showing up the different influence factors of a chemical reaction. The thermodynamic formulation is obtained here by assuming the exponential statistical distribution within each stable chemical state. The general model we obtain yields two stochastic formulations called the stochastic transition state theory (denoted STST) and the stochastic activated collision theory (denoted SACT) respectively, depending on whether the rate of the reaction is of the same scale as, either the rate of passing over the potential energy barrier, for the STST, or the rate of reaching the activated complex state (which is a generalization of the collision rate), for the SACT. The modeling is first done in the case of a closed small system undergoing stochastic changes of chemical state and then, by extension, in the frame of classical chemical kinetics. Some properties of these two theories are studied. Furthermore the formulation is applied to the stochastic example of RNA structure changes and to the classical simple example of a reaction between two atoms A and B to form the diatomic molecule AB.

This paper describes the formal verification of an interlocking system. We have formally proved the non-derailing and non-collision safety properties for an existing interlocking system operating on Paris Metro's line 3Bis. These high-level properties have first been refined to an intermediate level permitting their expression in terms of the control system's inputs and outputs. The resulting properties have then been formalised in the Prover iLock Verifier engine's internal language. The Prover iLock Verifier engine is a COTS commercialised by Prover Technology. For this project some specific features have been added to the engine to provide certified proofs that can be used, instead of testing, in the SIL-4 qualification process of interlocking systems.

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract This work presents a formal verification process based on the Systerel Smart Solver (S3) toolset for the development of safety-critical embedded software. In order to guarantee the correctness of the implementation of a set of textual requirements, the process integrates different verification techniques (inductive proof, bounded model checking, test case generation and equivalence proof) to handle different types of properties at their best capacities. It is aimed at the verification of properties at system, design, and code levels. To handle the floating-point arithmetic (FPA) in both the design and the code, an FPA library is designed and implemented in S3. This work is illustrated on an Automatic Rover Protection (ARP) system implemented on-board a robot. Focus is placed on the verification of safety and functional properties and on the equivalence proof between the design model and the generated code.

This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 18132Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract. In this paper, we integrate inductive proof, bounded model checking, test case generation and equivalence proof techniques to verify an embedded system. This approach is implemented using Systerel Smart Solver (S3) toolset. It is applied to verify properties at system, software, and code levels. The verification process is illustrated on an anti-collision system (ARP for Automatic Rover Protection) implemented on-board a rover. Focus is placed on the verification of safety and functional properties and the proof of equivalence between the design model and the generated code. To cite this version: