Tunis's New Mosques Constructed Between 1975 and 1995: Morphological Knowledge

The mosque has always been a prominent unit that used to structure the old Islamic cites. Its architecture through the Muslim world has always aroused the interest of many researchers. Actually, mosques are still built while undergoing the changes which occurred on the modern societies. However, only few research who have been interested in the new mosques. This paper targets the architecture of mosques built in Tunis governorate between 1975 and 1995. Through a morphological analysis of 24 mosques we were able to determine their identity and their morphological structure. According to their form and position, we discovered classes of specimen and classes of segments. Our corpus presents several constants and variations that we can explain though the introduction of some extrinsic attributes. In fact, these architectural objects possess some morphological specifications related to some urban, functional and historical factors

Fundamental Results on Automated Theorem Proving by Test Set Induction

We present in this paper a general scheme for test set induction procedure and describe a simple technique to prove the correctness of this procedure. Previously, we could only compute a test set for a conditional specification if the constructors were free. Here, we give a new definition of test sets and a procedure to compute them even if the constructors are not free. The method uses a new notion of provable inconsistency and induction prositions (that need to be instantiated by induction schemes) which allows us to refute more false conjectures than with previous approaches. We also present an algorithm to compute all the induction positions of a conditional specification. Finally, we propose an induction procedure which is refutationally complete for conditional specifications (not restricted to boolean specifications) in that it refutes any conjecture which is not an inductive theorem. The method has been implemented in SPIKE. Based on computer experiments, SPIKE appears to be more practical and efficient than related systems

Parameterized conditional specifications : sufficient completeness and implicit induction

Theorem proving in parameterized specifications allows for shorter and more structured proofs. Moreover, a generic proof can be given just once and reused for each instantiation of the parameters. We present procedures to test sufficient completeness and to prove and disprove inductive properties automatically in parameterized conditional specifications. Our method relies on the notion of test set, which can be seen as a well-suited induction scheme. Previously, we could only compute a test set for conditional specifications if the constructors were free. Here, we give a new definition of test sets and an algorithm to compute them even if the constructors are not free. The method uses a new notion of provable inconsistency which allows us to refute more false conjrectures than with previous approaches. This new method when limited to non parameterized conditional specifications, can refute general clauses, refutational completeness is also preserved for boolean ground convergent rewrite systems with completely defined functions even if the constructors are not free. The method has been implemented in the prover SPIKE. Based on computer experiments, the method appears to be more practical and efficient than inductive theorem proving in non-parameterized specifications

Implicit induction in conditional theories

We propose a new procedure for proof by induction in conditional theories where case analysis is simulated by term rewriting. This technique reduces considerably the number ofvariables of a conjecture to be considered for applying induction schemes (inductive positions). Our procedure is presented as a set of inference rules whose correctness has been formally proved. Moreover, when the axioms are ground convergent it is possible to apply the system for refuting conjectures. The procedure is even refutationally complete for conditional equations with boolean preconditions over free constructors (under the same hypotheses). The method is entirely implemented in the prover SPIKE. This system has proved interesting examples in a completely automatic way, that is, without interaction with the user and without ad-hoc heuristics. It has also proved the challenging Gilbreath card trick, with only 2 easy lemmas

Automatic Verification of Sufficient Completeness for Conditional Constrained Term Rewriting Systems

We present a procedure for checking sufficient completeness for conditional and constrained term rewriting systems with axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership...). Such axioms allow to specify complex data structures like e.g. sets, sorted lists or powerlists. Our method is integrated in a framework for inductive theorem proving based on tree grammars with constraints, a formalism which permits an exact representation of languages of ground constructor terms in normal form. The procedure is sound and complete. It has been successfully applied, yielding very natural proofs and, in case of negative answer, a counter example suggesting how to complete the specification. Moreover, it is a decision procedure when the TRS is unconditional but constrained, for a large class of constrained constructor axioms

Security Protocol Verification with Implicit Induction and Explicit Destructors

International audienceWe present a new method for automatic implicit induction theorem proving, and its application for the verification of a key distribution cryptographic protocol. The method can handle axioms between constructor terms, a feature generally not supported by other induction procedure. We use such axioms in order to specify explicit destructors representing cryptographic operators

Subependymome du ventricule lateral: presentation d’une serie de 5 cas et revue de la litterature.

Description Les subépendymomes sont des tumeurs bénignes rares, de découverte souvent fortuite et siégeant préférentiellement au niveau du quatrième ventricule, plus rarement au niveau du ventricule latéral.Objectif Le but de notre étude est de présenter notre expérience en matière de subépendymomes du ventricule latéral et de discuter leurs caractéristiques cliniques, radiologiques, de prise en charge et pronostiques au vu des données actuelles de la littérature.Méthode Etude rétrospective de cinq cas de subépendymomes symptomatiques du ventricule latéral pris en charge au sein de notre institution au cours des dix dernières années.Résultats Cinq sujets de sexe masculin avec des subépendymomes histologiquement prouvés ont été recensés. L’âge moyen était de 35.2 ans. La présentation clinique allait du début brutal avec aggravation rapide de l’état neurologique aux formes insidieuses avec syndrome d’hypertension intracrânienne évoluant depuis un an. La tumeur était confinée au ventricule latéral dans trois cas et étendue au troisième ventricule dans les deux autres cas avec une taille allant de 12 à 42 mm. L’exérèse complète par un abord trans calleux était réalisée dans tous les cas. L’évolution était favorable avec absence de récidive après un suivi moyen de 6 ans 2 mois.Conclusion Les subépendymomes du ventricule latéral sont rares, avec une symptomatologie variable et une évolution imprévisible. La chirurgie est la modalité thérapeutique de choix et l’exérèse totale doit être envisagée dans tous les cas.Mots clés : Chirurgie, Imagerie par résonance magnétique, Subépendymome, Ventricule latéral, Subépendymome, Ventricule latéra

Automated mathematical induction

Projet EURECAProofs by induction are important in many computer science and artifical intelligence applications, in particular, in program verification and specification systems. We present a new method to prove (and disprove) automatically inductives properties. Given a set of axioms, a well-suited induction scheme is constructed automatically. We call such and induction scheme a test set. Then, for proving a property, we just instantiate it with terms from the test set and apply pure algebraic simplifications to the result. This method needs no completion and explicit induction. However it retains their positive features, namely, the completeness of the former and the robustness of the latter. It has been implemented in the theorem-prover SPIKE