Related papers: Computing with Coloured Tangles
Graphical languages, like quantum circuits or ZX-calculus, have been successfully designed to represent (memoryless) quantum computations acting on a finite number of qubits. Meanwhile, delayed traces have been used as a graphical way to…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
Inspired by social networks and complex systems, we propose a core-periphery network architecture that supports fast computation for many distributed algorithms and is robust and efficient in number of links. Rather than providing a…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous…
This paper explores the computational complexity of diffusion-based language modeling. We prove a dichotomy based on the quality of the score-matching network in a diffusion model. In one direction, a network that exactly computes the score…
Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…
We present and explore a model of stateless and self-stabilizing distributed computation, inspired by real-world applications such as routing on today's Internet. Processors in our model do not have an internal state, but rather interact by…
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
In this paper, we revisit topological-like features in the extended Temperley--Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and entanglement swapping. We perform these quantum circuits…
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behaviour of cellular automata, that the computational basis…
We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges…
In the past couple of years a rich connection has been found between the fields of descriptive set theory and distributed computing. Frequently, and less surprisingly, finitary algorithms can be adopted to the infinite setting, resulting in…
This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…
We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure…
Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial…
We propose communication pattern logic. A communication pattern describes how processes or agents inform each other, independently of the information content. The full-information protocol in distributed computing is the special case…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell complex with vertices given by a representative subset of the point cloud. The vertex…