相关论文: Ordinal Recursion Theory

Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the…

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…

There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…

We derive the first ever on-shell recursion relations for amplitudes in effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to…

In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…

Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those…

Algorithmic recourse aims to provide actionable recommendations to individuals to obtain a more favourable outcome from an automated decision-making system. As it involves reasoning about interventions performed in the physical world,…

Uniform metastable convergence is a weak form of uniform convergence for a family of sequences. In this paper we explore the way that metastable convergence stratifies into a family of notions indexed by countable ordinals. We give two…

This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…

The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as…

We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its beta-function at one-loop with the use of the background field method. Thus…

We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…

In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…

We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…

In the course of many mathematical developments involving 'number systems' like $\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb {C}$ etc., it sometimes becomes necessary to abstract away and study certain properties of the number…

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying…

Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…

The increasing occurrence of ordinal data, mainly sociodemographic, led to a renewed research interest in ordinal regression, i.e. the prediction of ordered classes. Besides model accuracy, the interpretation of these models itself is of…

This article explores an operational model for transition amplitudes between measurements proposed by Goyal et al. within the quantum reconstruction program. To classify suitable amplitude algebras, we distinguish mathematical axioms,…

Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…