We have developed an algebraic framework for the study of recursion. For immediate linear recursion, a Horn clause is represented by a relational algebra operator. We show that the set of all such operators forms a closed semiring. In this formalism, query answering corresponds to solving a linear equation. For the first time, we are able to have the query answer expressed in an explicit algebr...

in order to have better insight of project characteristics, different kinds of fuzzy analysis for project networks have been recently proposed, most of which consider activities duration as the main and only source of imprecision and vagueness, but as it is usually experienced in real projects, the structure of the network is also subject to changes. in this paper we consider three types of imp...

We demonstrate a fully automated method for obtaining a closedform approximation of a recursive function. This method resulted from a realworld problem in which we had a detector that monitors a time series and where we needed an indication of the total number of false positives expected over a fixed amount of time. The problem, because of the constraints on the available measurements on the de...

In these notes we give an extensive survey of the recent progress for critical spread-out oriented percolation above the upper critical dimension. We describe the main tools, which are the lace expansion and the inductive method. The lace expansion gives a recursion relation for the two-point functions involved, and the inductive method gives an inductive analysis of the arising recursion relat...

Manna's theorem on (partial) correctness of programs essentially states that in the statement of the Floyd inductive assertion method, "A flow diagram is correct with respect to given initial and final assertions if suitable intermediate assertions can be found," we may replace "if" by "if and only if." In other words, the method is complete. A precise formulation and proof for the flow chart c...

Polarized SILL is a programming language that combines functional with session-typed message-passing concurrency. It features general recursion; code and channel transmission; synchronous asynchronous communication. To reason about programs, we develop the first program equivalence framework based on observable communications. We give meaning to programs using an observed communication semantic...

Tail-recursive function definitions are sometimes more straightforward than alternatives, but proving theorems on them may be roundabout because of the peculiar form of the resulting recursion induction rules. This paper describes a proof method that provides a general solution to this problem by means of suitable invariants over inductive sets, and illustrates the application of such method by...

In this communication we propose the use of the Augmented Space Recursion as an ideal methodology for the study of electronic and magnetic structures of rough surfaces, interfaces and overlayers. The method can take into account roughness, short-ranged clustering effects, surface dilatation and interdiffusion. We illustrate our method by an application of Fe overlayer on Ag (100) surface.

Novice Computer Science (CS) students struggle learning recursion for reasons such as unfamiliarity with recursive thinking and difficulty in visualizing program execution. Many tasks in CS require a thorough understanding of recursion. We introduce the recursion module of ChiQat-Tutor, an environment for learning CS algorithms and data structures. ChiQat-Tutor uses the pedagogical tool of Recu...

We prove that the Langmann-Szabo-Zarembo (LSZ) model with quartic potential, a toy for quantum field theory on noncommutative spaces grasped as complex matrix model, obeys topological recursion of Chekhov, Eynard and Orantin. By introducing two families correlation functions, one corresponding to meromorphic differentials $\omega_{g,n}$ recursion, we obtain Dyson-Schwinger equations eventually ...