Combining initial segments of lists

Combining Initial Segments of Lists

We propose a new way to build a combined list from K base lists, each containing N items. A combined list consists of top segments of various sizes from each base list so that the total size of all top segments equals N . A sequence of item requests is processed and the goal is to minimize the total number of misses. That is, we seek to build a combined list that contains all the frequently req...

Combining Lists with Integers?

Definability of Initial Segments

Let T be a first order theory formulated in the language L and P a new relation symbol not in L. Let φ(P ) be an L ∪ {P}-sentence. Let us say that φ(P ) defines P implicitly in T if T proves φ(P ) ∧ φ(P ) → ∀x(P (x) ↔ P (x)). Beth’s definability theorem states that if φ(P ) defines P implicitlly in T then P (x) is equivalent to an L-formula. However, if we consider implicit definability in a gi...

Combining Lists with Non-stably Infinite Theories

In program verification one has often to reason about lists over elements of a given nature. Thus, it becomes important to be able to combine the theory of lists with a generic theory T modeling the elements. This combination can be achieved using the Nelson-Oppen method only if T is stably infinite. The goal of this paper is to relax the stable-infiniteness requirement. More specifically, we p...

Lattice Initial Segments of the Turing Degrees

Lattice Initial Segments of the Turing Degrees