相关论文: Infinite time computable model theory

This work is motivated by the problem of finding the limit of the applicability of the first incompleteness theorem ($\sf G1$). A natural question is: can we find a minimal theory for which $\sf G1$ holds? We examine the Turing degree…

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…

The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing…

We show how tools from computational group theory can be used to prove that a subgroup of matrices has infinite index.

We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have…

A quantum gravity computer is one for which the particular effects of quantum gravity are relevant. In general relativity, causal structure is non-fixed. In quantum theory non-fixed quantities are subject to quantum uncertainty. It is…

Every mathematical structure has an elementary extension to a pseudo-countable structure, one that is seen as countable inside a suitable class model of set theory, even though it may actually be uncountable. This observation, proved easily…

We state a version of the P=?NP problem for infinite time Turing machines. It is observed that P not= NP for this version.

We develop a timeout based extension of propositional linear temporal logic (which we call TLTL) to specify timing properties of timeout based models of real time systems. TLTL formulas explicitly refer to a running global clock together…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

This article expands our work in [Ca16]. By its reliance on Turing computability, the classical theory of effectivity, along with effective reducibility and Weihrauch reducibility, is only applicable to objects that are either countable or…

Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…

We present a brief review on information processing, computing and inference via quantum fluctuation, and clarify the relationship between the probabilistic information processing and theory of quantum spin glasses through the analysis of…

We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our…

Time is a parameter playing a central role in our most fundamental modelling of natural laws. Relativity theory shows that the comparison of times measured by different clocks depends on their relative motion and on the strength of the…

In this paper, we investigate finite representations of DatalogMTL models. First, we discuss sufficient conditions for detecting programs that have finite models. Then, we study infinite models that eventually become constant and introduce…

We develop a realizability model in which the realizers are the reals not just Turing computable in a fixed real but rather the reals in a countable ideal of Turing degrees. This is then applied to prove several separation results involving…

Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…

We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between $\infty$-tilting objects in complete, cocomplete abelian categories with an…