Related papers: An Algebraic Treatment of Recursion
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
A monolithic process is a single recursive equation with data parameters, which only uses non-determinism, action prefixing, and recursion. We present a technique that decomposes such a monolithic process into multiple processes where each…
We usually define an algebraic structure by a set, some operations defined on this set and some propositions that the algebraic structure must validate. In some cases, we can replace these propositions by an algorithm on terms constructed…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
We find solutions for a linear deformation of the symmetric three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed relation are obtained. The new density (weight) function is…
The problem of giving a computational meaning to classical reasoning lies at the heart of logic. This article surveys three famous solutions to this problem - the epsilon calculus, modified realizability and the dialectica interpretation -…
In the article 'Ordinal Logics and the Characterizations of the Informal Concept of Proof', Georg Kreisel poses the problem of assigning unique notations to recursive ordinals, and additionally suggests that the methods which are developed…
Neither the classical nor intuitionistic logic traditions are perfectly-aligned with the purpose of reasoning about computation, in that neither tradition can permit unconstrained recursive definitions without inconsistency: recursive…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function…
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…
The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on…
Inspired by computability logic\cite{Jap03}, we refine recursive function definitions into two kinds: blindly-quantified (BQ) ones and parallel universally quantified (PUQ) ones. BQ definitions corresponds to the traditional ones where…
Natural language processing has greatly benefited from the introduction of the attention mechanism. However, standard attention models are of limited interpretability for tasks that involve a series of inference steps. We describe an…
Moore introduced a class of real-valued "recursive" functions by analogy with Kleene's formulation of the standard recursive functions. While his concise definition inspired a new line of research on analog computation, it contains some…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and…
The objectives of this research work which is intimately related to pattern discovery and management are threefold: (i) handle the problem of pattern manipulation by defining operations on patterns, (ii) study the problem of enriching and…