Many applications of automated deduction and verification require reasoning in combinations of theories, such as, on the one hand (some fragment of) first-order logic, and on, the other hand a background theory, such as some form of arithmetic. Unfortunately, due to the high expressivity of the full logic, complete reasoning is impossible in general. It is a realistic goal, however, to devise t...

We study the tessellation de ned as the intersection of two independent planar Poisson-Voronoi tessellations and derive the means of its main geometrical characteristics. For this intersection tessellation, we distinguish between six types of cells depending on whether they contain the nuclei of the two initial tessellations or not. The intensity and the mean area of each type of cell are compu...

Superposition-based provers have been successfully used to discharge proof obligations stemming from proof assistants. However, many such obligations require induction to be proved. We present a new extension of typed superposition that can perform structural induction. Several inductive goals can be attempted within a single saturation loop, by leveraging AVATAR [1]. Lemmas obtained by general...

The absence of a finite axiomatization of the first-order theory of datatypes and codatatypes represents a challenge for automatic theorem provers. We propose two approaches to reason by saturation in this theory: one is a conservative theory extension with a finite number of axioms; the other is an extension of the superposition calculus, in conjunction with axioms. Both techniques are refutat...

Rui M. R. de Bastos SUPERPOSITION RENDERING: Increased Realism for Interactive Walkthroughs (Under the direction of Dr. Frederick P. Brooks, Jr.) The light transport equation, conventionally known as the rendering equation in a slightly different form, is an implicit integral equation, which represents the interactions of light with matter and the distribution of light in a scene. This research...

The first-order theory over non-linear arithmetic including transcendental functions (NLA) is undecidable. Nevertheless, in this paper we show that a particular combination with superposition leads to a sound and complete calculus that is useful in practice. We follow basically the ideas of the SUP(LA) combination, but have to take care of undecidability, resulting in “unknown” answers by the N...

We present practical codes designed for the Gaussian dirty paper (Costa) channel. We show that the dirty paper decoding problem can be transformed into an equivalent multiple-access problem, for which we apply superposition coding. Our approach is a generalization of the nested lattices approach of Zamir, Shamai and Erez. We present simulation results which confirm the effectiveness of our meth...

Real and bounded elliptic solutions suitable for applying the KhareSukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified KadomtsevPetviashvili equation (gmKPE) and the nonlinear cubic-quintic Schrödinger equation (NLCQSE).

This paper deals with decision procedures specified by using a superposition calculus which is an inference system at the core of all equational theorem provers. This calculus is refutation complete: it provides a semi-decision procedure that halts on unsatisfiable inputs but may diverge on satisfiable ones. Fortunately, it may also terminate for some theories of interest in verification, and t...