Related papers: Space and Time Complexity for Infinite Time Turing…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
Reachability and LTL model-checking problems for flat counter systems are known to be decidable but whereas the reachability problem can be shown in NP, the best known complexity upper bound for the latter problem is made of a tower of…
This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…
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…
Infinite Time Register Machines ($ITRM$'s) are a well-established machine model for infinitary computations. Their computational strength relative to oracles is understood, see e.g. Koepke (2009), Koepke and Welch (2011) and Koepke and…
Space and time are central concepts for understanding our World. They are important ingredients at the core of every scientific theory and subject of intense debate in philosophy. Albert Einstein's Special and General theories of Relativity…
Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
The recent suggestion that late time quantum dynamics may be important for resolving cosmological issues associated with our observed universe requires a consideration of several subtle issues associated with quantum cosmology, as we…
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic. Counting word models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of…
As repeatedly emphasized by Einstein our knowledge of the structure of space and time is based entirely on inferences from observations of physical objects and processes. At the most fundamental level these objects and processes are…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
Inspired by the notion that physical systems can contain only a finite amount of information or complexity, we introduce a framework that allows for quantifying the amount of logical information needed to specify a function or set. We then…
This paper extends our paper \cite{C2} for the conference ``Computability in Europe'' 2022. After Infinite Time Turing Machines (ITTM) were introduced in Hamkins and Lewis \cite{HL}, a number of machine models of computability have been…
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…
We study in detail the moduli space of solutions discovered in LLM relaxing the constraint that guarantees the absence of singularities. The solutions fall into three classes, non-singular, null-singular and time machines with a time-like…
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…
In this paper, we study strengthenings of Infinite Times Blum-Shub-Smale-Machines (ITBMs) that were proposed by Seyfferth in [14] and Welch in [15] obtained by modifying the behaviour of the machines at limit stages. In particular, we study…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…