Scenario-based specifications such as message sequence charts (MSC) offer an intuitive and visual way to describe design requirements. MSC-graphs allow convenient expression of multiple scenarios, and can be viewed as an early model of the system that can be subjected to a variety of analyses. Problems such as LTL model checking are undecidable for MSC-graphs in general, but are known to be dec...

In this note we exhibit a continuity principle for real-valued functions on C[−1, 1] that is not validated by realizability over domains although it is validated by Kleene’s functional realizability corresponding to Weihrauch’s theory of type 2 effectivity. Mathematics Subject Classification: 03F50, 03F60, 18C50, 06B35.

Let V be a set of number-theoretical functions. We define notion absolute -realizability for predicate formulas and sequents in such way that the indices functions are used interpreting implication universal quantifier. In this article, we prove Basic Predicate Calculus is sound with respect to semantics if satisfies some natural conditions.

We show how different functional interpretations can be combined via a multi-modal linear logic. A concrete hybrid of Kreisel’s modified realizability and Gödel’s Dialectica is presented, and several small applications are given. We also discuss how the hybrid interpretation relates to variants of Dialectica and modified realizability with non-computational quantifiers.

This paper studies fundamental analytic properties of generating series for nonlinear control systems, and of the operators they deene. It then applies the results obtained to the extension of facts, which relate realizability and algebraic input/output equations, to local realizability and analytic equations.

The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but difficult to implement with high-order numerical methods. regularized was recently introduced remove one of main challenges implementation method, namely requirement realizability solution. In this work we use relative entropy prove co...

We construct a universal and even logically fully abstract realizability model for the sequential functional programming language of call-by-name FPC. This model is defined within the category of modest sets over the total combinatory algebra L of observational equivalence classes of closed terms of the untyped programming language λ+Error. This language is untyped lazy call-by-name lambda-calc...

In the paper we study the problem of the isotropic realizability in R2 of a regular strain field e(U) = 12 ( DU +DU ) for the incompressible Stokes equation, namely the existence of a positive viscosity μ > 0 solving the Stokes equation in R2 with the prescribed field e(U). We show that if e(U) does not vanish at some point, then the isotropic realizability holds in the neighborhood of that poi...