Related papers: Unary Primitive Recursive Functions
Abstract models of computation often treat the successor function $S$ on $\mathbb{N}$ as a primitive operation, even though its low-level implementations correspond to non-trivial programs operating on specific numerical representations.…
A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
We study Basic Arithmetic, BA introduced by W. Ruitenburg. BA is an arithmetical theory based on basic logic which is weaker than intuitionistic logic. We show that the class of the provably total recursive functions of BA is a proper…
We study existence, uniqueness and computability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences---one that analyzes principal eigenvalues of…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Combinatorial properties of maximal repetitions (runs) in formal words are studied. We classify all maximal repetitions in a word as primary and secondary where the set of all primary repetitions determines all the other repetitons in the…
In this article, variational state estimation is examined from the dynamic programming perspective. This leads to two different value functional recursions depending on whether backward or forward dynamic programming is employed. The result…
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of…
We study the possibility to reconstruct the primordial function for some periodic function. The procedure includes an analytical continuation of a discrete function for Fourier coefficients computation, that introduces an ambiguity. To…
It is well known that many theorems in recursion theory can be "relativized". This means that they remain true if partial recursive functions are replaced by functions that are partial recursive relative to some fixed oracle set. Uspensky…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
In this work, we study vector-valued functional equations with multiple recursive terms that arise naturally when we are dealing with vector-valued multiplicative Lindley-type recursions. We provide a detailed framework for the solution of…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
We determine sufficient conditions under which certain recursively defined functions are well defined for all real inputs. Given a function $f:\mathbb R\to\mathbb R$, call a decreasing sequence $x_1>x_2>x_3>\cdots$ "$f$-bad" if…
Results on two different settings of asymptotic behavior of approximation characteristics of individual functions are presented. First, we discuss the following classical question for sparse approximation. Is it true that for any individual…
Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely…
The paper discusses several extensions of the recursive representation of the flow shop scheduling problem. It is shown that recursive functions make it possible to describe multiple extensions in a single problem. The paper considers…