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Complétude pour les demi-anneaux et algèbres de Kleene étoile-continues avec domaine
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mbacke, Sokhna Diarra |
| Copyright Year | 2018 |
| Abstract | Due to their increasing complexity, today’s computer systems are studied using multiple models and formalisms. Thus, it is necessary to develop theories that unify di erent approaches in order to limit the risks of errors when moving from one formalism to another. It is in this context that monoids, semirings and Kleene algebras with domain were born about a decade ago. The idea is to de ne a domain operator on classical algebraic structures, in order to unify algebra and the classical logics of programs. The question of completeness for these algebras is still open. It constitutes the object of this thesis. We de ne tree structures called trees with a top and represented in matrix form. After having given fundamental properties of these trees, we de ne relations that make it possible to compare them. Then, we show that, modulo a certain equivalence relation, the set of trees with a top is provided with a monoid with domain structure. This result makes it possible to de ne a model for semirings with domain and prove its completeness. We also de ne a model for ∗-continuous Kleene algebras with domain as well and prove its completeness modulo a new axiom. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www2.ift.ulaval.ca/~desharnais/Recherche/Theses/memoire.Sokhna.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
