A bstract We construct the off-shell recursion for gravity and graviton current perturbative double field theory (DFT). first formulate DFT, which is equivalent but simpler to general relativity, all-orders in fluctuations of generalised metric. The action equations motion (EoM) are derived arbitrary order pure case. then derive recursion, counterpart Berends-Giele Yang-Mills theory, through so...

This paper describes a generic method to derive an animation from a recursive definition, with the objective of debugging and understanding this definition by expliciting its control structure. This method is based on a well known algorithm of factorizing a recursive function into the composition of the producer and the consumer of its call tree. We developed a systematic method to transform bo...

Dwarf is a highly compressed structure, which compresses the cube by eliminating the semantic redundancies while computing a data cube. Although it has high compression ratio, Dwarf is slower in querying and more difficult in updating due to its structure characteristics. We all know that the original intention of data cube is to speed up the query performance, so we propose two novel clusterin...

A general method to map a polynomial recursion on a matrix linear one is suggested. The solution of the recursion is represented as a product of a matrix multiplied by the vector of initial values. This matrix is product of transfer matrices whose elements depend only on the polynomial and not on the initial conditions. The method is valid for systems of polynomial recursions and for polynomial...

Recursion is a complex concept that most novice logic programmers have difficulty grasping. Problems associated with recursion are avoided in imperative languages where iteration is provided as an alternative to recursion. Although difficult to learn, recursion is very easy to use once it is understood. In fact, many problems that have straightforward recursive solutions have very sophisticated...

The traditional program refinement strategy cannot be refined to an executable program, and there are issues such as low verification reliability automation. To solve the above problems, this paper proposes a nonlinear construction method based on partition recursion Morgan's rules. First, we use recursive definition technique characterize initial specification. specification is then transforme...

We introduce a variant of Spector’s bar recursion (called “modified bar recursion”) in finite types to give a realizability interpretation of the classical axiom of countable choice allowing for the extraction of witnesses from proofs of Σ1 formulas in classical analysis. As a second application of modified bar recursion we present a bar recursive definition of the fan functional. Moreover, we ...

We give a recursion-theoretic characterization of the complexity classes NC for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computati...

Context: In software engineering, taking a good election between recursion and iteration is essential because their efficiency and maintenance are different. In fact, developers often need to transform iteration into recursion (e.g., in debugging, to decompose the call graph into iterations); thus, it is quite surprising that there does not exist a public transformation from loops to recursion ...