Improving Strategies via SMT Solving

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Pi-p-2-complete

Recherche des hémoglobinopathies qualitatives chez les hémophiles à Abidjan, Côte d’Ivoire

Introduction : L’hémophilie est une maladie héréditaire rare à transmission récessive liée au chromosome X. Les principaux  symptômes sont l’hémorragie, les hématomes, l’anémie et les douleurs articulaires dans les hémarthroses. Ces deux derniers signespeuvent se retrouver au cours des hémoglobinopathies. Ainsi, l’objectif de cette étude était de rechercher la présence d’hémoglobinopathies qualitatives dans une cohorte d’hémophiles suivis au service d’hématologie clinique du CHU de Yopougon.Méthodes : C’est une étude transversale qui s’est déroulée de Janvier à Juillet 2017 au niveau de l’unité d’hématologie du laboratoire central du CHU de Yopougon. Sur les prélèvements de 49 patients, ont été effectués l’hémogramme, l’électrophorèse de l’hémoglobine, le taux de prothrombine (TP), le temps de céphaline activée (TCA) et le dosage des facteurs VIII et IX par la méthode chronométrique.Résultats : La moyenne d’âge était de 17 ans avec 73,5% d’élèves et étudiants. Les hémarthroses (75,5%) et les hématomes (36,7%) constituaient l’essentiel des signes cliniques. La complication majeure était la déformation articulaire à 34,7%. Sur les 49 patients constituant la cohorte, le pourcentage d’hémophiles A était de 89.8% (44/49) et celui d’hémophiles B 10,2% (5/49), avec 81,6% (40/49) d’hémophiles sévères. La fréquence des hémoglobinopathies qualitatives est de 8,2% (4/49) avec 6,2% de trait drépanocytaire AS (3/49) et 2% d’hémoglobine AC (1/49).Conclusion : Cette étude a mis en évidence la présence d’hémoglobinopathies qualitatives, pouvant coexister avec l’hémophilie, ce qui peut compliquer la prise en charge et la qualité de vie des patients. Mots clés : Hémophilie, hémogramme, électrophorèse, Abidjan.   English title: Research of qualitative haemoglobinopathies in hemophiliacs in Abidjan, Côte d’Ivoire Introduction: Hemophilia is a rare hereditary disease with X-linked recessive inheritance. The main symptoms are haemorrhage, hematoma, anemia and joint pain associated with hemarthrosis. These last two signs can also be found during haemoglobinopathies. Thus, the objective of this study was to investigate the presence of qualitative haemoglobinopathies in a cohort of hemophiliacs followed in the clinical hematology department of Yopougon University Hospital. Methods: This is a cross-sectional study that took place from January to July 2017 at the hematology unit of the central laboratory of the Yopougon University Hospital. On the samples of 49 patients, blood count, haemoglobin electrophoresis, prothrombin time (PT), activated partial thromboplastin time (APTT) and factor VIII and IX were measured by the chronometric method. Results: The average age was 17 with 73.5% of students. Haemarthrosis (75.5%) and hematoma (36.7%) constituted the bulk of clinical signs. The major complication was joint deformity with 34.7%. Of the 49 patients in the cohort, the proportion of hemophiliacs A was 89.8% (44/49) and that of hemophiliac B was 10.2% (5/49), with 81.6% (40/49) of all patients showing severe haemophilia. The frequency of qualitative haemoglobinopathies was 8.2% (4/49) with 6.2% of haemoglobin AS or sickle cell trait (3/49) and 2% of haemoglobin AC (1/49). Conclusion: This study highlighted the presence of qualitative hemoglobinopathies that can coexist with hemophilia, which can  complicate the management and quality of life of patients. Keywords: Hemophilia, hemogram, electrophoresis, Abidjan.  &nbsp