Related papers: On the computability of graph Turing machines
The joint degree matrix of a graph gives the number of edges between vertices of degree i and degree j for every pair (i,j). One can perform restricted swap operations to transform a graph into another with the same joint degree matrix. We…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Kautz and de Bruijn graphs have a high degree of connectivity which makes them ideal candidates for massively parallel computer network topologies. In order to realize a practical computer architecture based on these graphs, it is useful to…
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…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to…
Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…
The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
Multiway Turing machines (also known as nondeterministic Turing machines or NDTMs) with explicit, simple rules are studied. Even very simple rules are found to generate complex behavior, characterized by complex multiway graphs, that can be…
We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog…
Partite, $3$-uniform hypergraphs are $3$-uniform hypergraphs in which each hyperedge contains exactly one point from each of the $3$ disjoint vertex classes. We consider the degree sequence problem of partite, $3$-uniform hypergraphs, that…
The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are…
In computable analysis, sequences of rational numbers which effectively converge to a real number x are used as the (rho-) names of x. A real number x is computable if it has a computable name, and a real function f is computable if there…
In this work, we survey the role of GPUs in real-time systems. Originally designed for parallel graphics workloads, GPUs are now widely used in time-critical applications such as machine learning, autonomous vehicles, and robotics due to…
We study an abstract group of reversible Turing machines. In our model, each machine is interpreted as a homeomorphism over a space which represents a tape filled with symbols and a head carrying a state. These homeomorphisms can only…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
Let $G$ be a connected graph and $\mathcal{P}(G)$ a graph parameter. We say that $\mathcal{P}(G)$ is feasible if $\mathcal{P}(G)$ satisfies the following properties: (I) $\mathcal{P}(G)\leq \mathcal{P}(G_{uv})$, if $G_{uv}=G[u\to v]$ for…
This paper examines conceptual models and their application to computational thinking. Computational thinking is a fundamental skill for everybody, not just for computer scientists. It has been promoted as skills that are as fundamental for…