Proving Reachability-Logic Formulas Incrementally

International audienceReachability Logic (RL) is a formalism for defining the operational semantics of programming languages and for specifying program properties. As a program logic it can be seen as a language-independent alternative to Hoare Logics. Several verification techniques have been proposed for RL, all of which have a circular nature: the RL formula under proof can circularly be used as a hypothesis in the proof of another RL formula, or even in its own proof. This feature is essential for dealing with possibly unbounded repetitive behaviour (e.g., program loops). The downside of such approaches is that the verification of a set of RL formulas is monolithic, i.e., either all formulas in the set are proved valid, or nothing can be inferred about any of the formula's validity or invalidity. In this paper we propose a new, incremental method for proving a large class of RL formulas. The proposed method takes as input a given RL formula under proof (corresponding to a given program fragment), together with a (possibly empty) set of other valid RL formulas (e.g., already proved using our method), which specify sub-programs of the program fragment under verification. It then checks certain conditions are shown to be equivalent to the validity of the RL formula under proof. A newly proved formula can then be incrementally used in the proof of other RL formulas, corresponding to larger program fragments. The process is repeated until the whole program is proved. We illustrate our approach by verifying the nontrivial Knuth-Morris-Pratt string-matching program

HVM BIOFLUX Human & Veterinary Medicine International Journal of the Bioflux Society Diagnostic particularities in Wilson's disease as related to age, sex and clinical presentation

Abstract. Objective: Wilson's disease (WD) is a genetic, autosomal recessive disorder, which affects the liver, brain and cornea. The condition is rare and it has various presentations, hence its diagnosis is difficult. We aimed to study different clinical presentations, their relation with age and sex and the influence of several factors on the diagnostic score (Leipzig score). Material and Methods: We analyzed retrospectively the medical documents of 24 WD patients examined in 2 nd Pediatric Clinic and 5 th Medical Clinic of Cluj-Napoca, and we collected data concerning the diagnosis. The patients were classified phenotypically (Leipzig classification) and we calculated the Leipzig score. We studied the relation between diagnostic score, clinical phenotype, age at diagnosis and sex. Results: Our group consisted of 7 adults and 17 pediatric patients, F/M = 1/1.4. They were distributed, according to the phenotype, as follows: acute hepatic (H1) -3 (pediatric, all deceased); chronic hepatic (H2) -12 (2 adults, 10 pediatric); neurological and hepatic (N1) -6 (3 adults, 3 pediatric), neurological (N2) -3 (2 adults, 1 pediatric). The hepatic involvement was inversely correlated with age (p=0.02), which in turn was directly correlated with neurological manifestations (p=0.05). There were no significant differences concerning either distribution on phenotypes in relation with sex and age or between Leipzig score and age, sex, onset modality, presence and severity of hepatic involvement. Conclusion: The presence of hepatic manifestations at the moment of diagnosis of WD decreases with age, while neurological one increases. The distribution on phenotypes was not influenced by age or sex. There is no relation between diagnostic score and studied demographical and clinical factors. Key Words: Wilson's disease, Wilson's disease clinical phenotypes, Leipzig score. Rezumat. Obiectiv: Boala Wilson (BW) este o afecţiune genetică, autosomal recesivă, care afectează ficatul, creierul şi corneea. Fiind foarte rară şi variabilă ca prezentare clinică, diagnosticul ei este dificil. Ne-am propus să studiem diferitele modalităţi de prezentare clinică, relaţia lor cu vârsta şi sexul pacienţilor şi influenţa mai multor factori asupra scorului diagnostic (scorul Leipzig). Material si metodă: Am analizat retrospectiv documentele medicale ale 24 pacienţi cu BW consultaţi în Clinicile Pediatrie II şi, respectiv, Medicală V, din Cluj-Napoca, culegând o serie de date privind diagnosticul. Pacienţii au fost clasificaţi fenotipic (clasificarea Leipzig) şi am calculat scorul Leipzig. Am studiat relaţia între scorul diagnostic, fenotipurile clinice, vârsta la diagnostic şi sexul pacienţilor. Rezultate: Lotul a cuprins 7 pacienţi adulţi şi 17 pediatrici, F/M = 10/14. Distribuţia pacienţilor pe fenotipuri a fost următoarea: hepatică acută (H1) -3 (pediatrici, decedaţi toţi); hepatică cronică (H2) -12 (2 adulţi, 10 pediatrici); neurologică şi hepatică (N1) -6 (3 adulţi, 3 pediatrici), neurologică (N2) -3 (2 adulţi, 1 pediatric). Prezenţa afectării hepatice s-a corelat invers cu vârsta (p=0,02), pe când manifestările neurologice au fost în relaţie directă cu vârsta (p=0,05). Nu au existat diferenţe semnificative privind distribuţia pe fenotipuri în raport cu vârsta sau sexul pacienţilor, nici între scorul Leipzig şi vârstă, sex, modalitatea de debut, prezenţa şi severitatea afectării hepatice. Concluzii: Prezenţa manifestărilor hepatice la momentul diagnosticului BW descreşte cu vârsta, pe când cea a manifestărilor neurologice creşte. Distribuţia pe fenotipuri nu este influenţată de vârstă sau sex. Nu exista o relaţie între scorul diagnostic şi factorii demografici şi clinici studiaţi. Cuvinte cheie: Boala Wilson, fenotipurile clinice de boala Wilson, scorul Leipzig

P transducers

10.1007/BF03037291New Generation Computing2411-28NGCO