Operators that systematically produce more precise abstract interpretations from simpler ones are interesting. In this paper we present a formal study of one such operator: the powerset. The main achievements of the paper are described below: • A formal definition of the powerset operator is given. For any given abstract interpretation D = 〈D, o1, . . . , ok〉, where D is the abstract domain and...

In this paper, having introduced a convergence of series on the root vectors in Abel-Lidskii sense, we present valuable application to evolution equations. The main issue paper is an approach allowing us principally broaden conditions imposed upon second term equation abstract Hilbert space. way, come definition function unbounded non-selfadjoint operator. Meanwhile, considering involve additio...

Following earlier work, a modal logic for T -coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yie...

We present a calculus with dependent types, subtyping and late-bound overloading. Besides its theoretical interest this work is motivated by several practical needs that range from the definition of logic encodings, to proof specialization and reuse, and to object-oriented extension of the SML module system. The theoretical study of this calculus is not straightforward. While confluence is rela...

In recent years there has been a lot of interest in the definition of so-called weakly-relational numeric domains, whose complexity and precision are in between the (non-relational) abstract domain of intervals [9] and the (relational) abstract domain of convex polyhedra [10]. The first weakly-relational domain proposed in the literature is based on systems of constraints of the form x−y ≤ c an...

In recent years there has been a lot of interest in the definition of so-called weakly-relational numeric domains, whose complexity and precision are in between the (non-relational) abstract domain of intervals [9] and the (relational) abstract domain of convex polyhedra [10]. The first weakly-relational domain proposed in the literature is based on systems of constraints of the form x−y ≤ c an...