Related papers: Computability Theory of Closed Timelike Curves
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers.…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
We investigate the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding…
This essay explores the limits of Turing machines concerning the modeling of minds and suggests alternatives to go beyond those limits.
Deutsch proposed two sorts of models of quantum computers, quantum Turing machines (QTMs) and quantum circuit families (QCFs). In this paper we explore the computational powers of these models and re-examine the claim of the computational…
Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…
In this paper we consider the computational complexity of uniformizing a domain with a given computable boundary. We give nontrivial upper and lower bounds in two settings: when the approximation of boundary is given either as a list of…
In the context of Markov decision processes running in continuous time, one of the most intriguing challenges is the efficient approximation of finite horizon reachability objectives. A multitude of sophisticated model checking algorithms…
Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…
We consider the region of closed timelike curves (CTC's) in three-dimensional flat Lorentz spacetimes. The interest in this global geometrical feature goes beyond the purely mathematical. Such spacetimes may be considered lower-dimensional…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking…
We extend the argument that spacetimes generated by two timelike particles in D=3 gravity (or equivalently by parallel-moving cosmic strings in D=4) permit closed timelike curves (CTC) only at the price of Misner identifications that…
This paper analyzes infinitary nondeterministic computability theory. The main result is D $\ne$ ND $\cap$ coND where D is the class of sets decidable by infinite time Turing machines and ND is the class of sets recognizable by a…
The study of very large graphs is a prominent theme in modern-day mathematics. In this paper we develop a rigorous foundation for studying the space of finite labelled graphs and their limits. These limiting objects are naturally countable…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…