Regularity is a shared memory consistency condition that has received considerable attention, notably in connection with quorum-based shared memory. Lamport's original definition of regularity assumed a single-writer model, however, and is not well defined when each shared variable may have multiple writers. In this thesis, we address this need by formally extending the notion of regularity to a multi-writer model. We have shown that the extension is not trivial. While there exist various ways to extend the single-writer definition, the resulting definitions will have different strengths. Specifically, we give several possible definitions of regularity in the presence of multiple writers. We then present a quorum-based algorithm to implement each of the proposed definitions and prove them correct. We study the relationships between these definitions and a number of other well-known consistency conditions, and give a partial order describing the relative strengths of these consistency conditions. Finally, we provide a practical context for our results by studying the correctness of two well-known algorithms for mutual exclusion under each of our proposed consistency conditions.

Regularity is a shared memory consistency condition that has received considerable attention, notably in connection with quorum-based shared memory. Lamport's original definition of regularity assumed a single-writer model, however, and is not well defined when each shared variable may have multiple writers. In this thesis, we address this need by formally extending the notion of regularity to a multi-writer model. We have shown that the extension is not trivial. While there exist various ways to extend the single-writer definition, the resulting definitions will have different strengths. Specifically, we give several possible definitions of regularity in the presence of multiple writers. We then present a quorum-based algorithm to implement each of the proposed definitions and prove them correct. We study the relationships between these definitions and a number of other well-known consistency conditions, and give a partial order describing the relative strengths of these consistency conditions. Finally, we provide a practical context for our results by studying the correctness of two well-known algorithms for mutual exclusion under each of our proposed consistency conditions.

En imagerie par transmission de rayons X, les mesures effectuées relèvent d'un opérateur intégral : la transformée de Radon en géométrie parallèle et la transformée conique en géométrie divergente. La caractérisation de l'image de ces opérateurs par des conditions de rang permet de quantifier l'incohérence des données mesurées par rapport au modèle intégral. Le premier volet de ce travail de thèse étudie les conditions de rang en géométrie conique~: nous proposons de nouvelles conditions pour une trajectoire planaire et mettons à jour des relations non triviales entre des conditions 2D et des conditions basées sur le théorème de Grangeat. Le second volet porte sur l'auto-étalonnage géométrique des systèmes tomographiques à géométrie conique. L'analyse des conditions de rang couplée au modèle géométrique des projections radiographiques permet la détermination de la géométrie d'acquisition du système. / In X-ray transmission imaging, the collected measurements correspond to an integral operator: the Radon transform in parallel geometry and the divergent beam transform in divergent geometry. The range of these operators is characterized by conditions, which help to quantify the consistency of the measured data with the forward integral model. The first pillar of this PhD work studies range conditions in cone-beam acquisition geometry: we derive new conditions for a planar trajectory and establish a new relation between 2D fanbeam conditions and Grangeat-based conditions. The second pillar is related to the self-calibration of cone-beam systems. The acquisition geometry of the system is determined from range conditions and a parametric model of the projection geometry.