We propose and investigate a formal language operation inspired by the naturally occurring phenomenon of DNA primer extension by a DNAtemplate-directed DNA Polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called template) the result of the primer extension is a DNA ...

The ultrapower T * of an arbitrary ordered set is introduced as infinitesimal extension . It obtained the equivalence classes sequences in , where corresponding relation generated by a free ultrafilter on natural numbers. established that always satisfies Cantor’s property, while one can give necessary and sufficient conditions for so would be complete or it fulfill open completeness respective...

We extend broadly studied rewrite transition systems with the mechanism for computing with partial information in the form similar to the one used in concurrent constraint programming. Two new classes of transition systems (fcBPA and fcBPP) are introduced as this extension changes expressibility power of rewrite transition systems corresponding to BPA and BPP. The power of rewrite systems corre...

Open computer-integrated facilities management systems hold the promise to improve facilities management practice, but they require extensive underlying technical foundations: particularly standardized data models to enable information sharing among computer applications. The International Alliance for Interoperability is developing Industry Foundation Classes to provide this type of support fo...

We introduce state classes, a construct to program objects that can be safely concurrently accessed. State classes model the notion of object’s state (intended as some abstraction over the value of fields) that plays a key role in concurrent object-oriented programming (as the state of an object changes, so does its coordination behavior). We show how state classes can be added to Java-like lan...

There are characteristic classes that are the obstructions to the vanishing of the differentials in the Lyndon-Hochischild-Serre spectral sequence of an extension of an integral lattice L by a group G. These characteristic classes exist in the r-th page of the spectral sequence provided differentials di = 0 for all i < r. If L further decomposes into a sum of G-sublattice L = L ⊕ L, we show tha...

We survey ultradifferentiable extension theorems, i.e., quantitative versions of Whitney's classical theorem, with special emphasis on the existence continuous linear operators. The focus is Denjoy-Carleman classes for which we develop theory from scratch and discuss important related concepts such as (non-)quasianalyticity. It allows us to give an efficient and, a fair extent, elementary intro...

Context. An extension method is a method declared in a package other than the package of its host class. Thanks to extension methods, developers can adapt to their needs classes they do not own: adding methods to core classes is a typical use case. This is particularly useful for adapting software and therefore to increase reusability. Inquiry. In most dynamically-typed languages, extension met...