Related papers: Kleene's Two Kinds of Recursion
The so-called tuned-correlated kernel (sometimes also called the first-order stable spline kernel) is one of the most widely used kernels for the regularized impulse response estimation. This kernel can be derived by applying an exponential…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
We answer a question of Slaman and Steel by showing that a version of Martin's conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin's…
With one exception, our previous work on recurrence extraction and denotational semantics has focused on a source language that supports inductive types and structural recursion. The exception handles general recursion via an initial…
There are two general irreversibility theorems for the renormalization group in more than two dimensions: the first one is of entropic nature, while the second one, by Forte and Latorre, relies on the properties of the stress-tensor trace,…
Binary Balanced Tree RvNNs (BBT-RvNNs) enforce sequence composition according to a preset balanced binary tree structure. Thus, their non-linear recursion depth is just $\log_2 n$ ($n$ being the sequence length). Such logarithmic scaling…
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…
We study a class of constrained reinforcement learning (RL) problems in which multiple constraint specifications are not identified before training. It is challenging to identify appropriate constraint specifications due to the undefined…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…
The cut-elimination method CERES (for first- and higher-order classical logic) is based on the notion of a characteristic clause set, which is extracted from an LK-proof and is always unsatisfiable. A resolution refutation of this clause…
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…
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
This note compares two approaches both alternatively used when establishing normality theorems in univariate Extreme Value Theory. When the underlying distribution function ($df$) is the extremal domain of attraction, it is possible to use…
Turing's famous 'machine' model constitutes the first intuitively convincing framework for computing with real numbers. Kleene's computation schemes S1-S9 extend Turing's approach and provide a framework for computing with objects of any…
In this article, we discuss a new version of metric fixed point theory especially of Banach Contraction Principle, Ran-Reurings Theorem and others.
The main result is a generalization of Keller's recursion equation for finding a prime number given the previous primes. We also examine the convergence of the limit in Keller's equation and the convergence of the limit in the general…
Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm oscillation theorem for systems of…
The best developed formulation of closed system quantum theory that handles multiple-time statements, is the consistent (or decoherent) histories approach. The most important weaknesses of the approach is that it gives rise to many…