Let As be the product of the first s primes, let Ps be the set of primes p for which p−1 divides As but p does not divide As, and let Cs be the set of Carmichael numbers n such that n is composed entirely of the primes in Ps and such that As divides n − 1. Erdős argued that, for any ε > 0 and all sufficiently large x (depending on the choice of ε), the set Cs contains more than x1−ε Carmichael ...

Interpretation The topic of static analysis, abstract interpretation and WCET analysis is quite big, there are several conferences with related material and so forth. This section will be focusing on central literature in my particular work. Since my work will be centralized around abstract interpretation, there is one important seminal paper, that is the introduction paper by Cousots in 1977. ...

We investigate some graph properties which may simplify the computation of the steady-state distribution of Markov chain. We consider the directed graph associated to a Markov chain derived from Stochastic Automata Network and we give an algorithm to solve the Kolmogorov equations for the steady-state distribution. Then, we present an extension of this algorithm which allows the parametric anal...

Proving that an uncertain parametric model is stable amounts to prove the inclusion of two sets: the set A of all feasible parameters and the set B of all parameters for which the model is stable. In this paper, a new algorithm, able to decide whether or not A is included in B, is presented. The method is based on interval analysis which is a numerical tool able to deal with inequalities in a g...

In this paper, we propose the use of lexicographic parametric programming to recognize efficient units in Data Envelopment Analysis (DEA). By using the parameterization of the rhs vector of the envelopment problem, we obtain the efficiency curve which is traversing through the efficient frontier from unit to unit. The units in the basis with any parameter value are efficient and the unit domina...

This article presents two methods of testing the hypothesis of equality of two functions H(0):f(1)(t)=f(2)(t) for all t, in a generalized non-parametric regression framework using a recently developed generalized non-parametric regression method called Bayesian adaptive regression splines (BARS). Of particular interest is the special case of testing equality of two Poisson process intensity fun...

Parametric static analysis allows choosing a parameter value tobalance the precision and cost of the instantiated analysis. Wepropose an efficient approach to either find a cheapest parame-ter value to prove a given query or show that no such parame-ter value exists. Our approach is based on refinement, as in CE-GAR (counterexample-guided abstraction refinement), but applies...

Shape analysis is a technique for providing static guarantees of properties of the heap during the execution of a program that manipulates dynamically allocated storage though destructive updating of pointers. It is interesting because of the widespread use of pointers, because of the difficulty of programming with pointers, and because of the intricate and severe errors that may follow from fl...