Related papers: Continuous and monotone machines
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…
Transformer-based models have dramatically increased their size and parameter count to tackle increasingly complex tasks. At the same time, there is a growing demand for high performance, low-latency inference on devices with limited…
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this…
Dependently typed languages such as Coq are used to specify and verify the full functional correctness of source programs. Type-preserving compilation can be used to preserve these specifications and proofs of correctness through…
In analogy to Brownian computers we explicitly show how to construct stochastic models, which mimic the behaviour of a general purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation,…
We build on a fine-grained analysis of session-based interaction as provided by the linear logic typing disciplines to introduce the SAM, an abstract machine for mechanically executing session-typed processes. A remarkable feature of the…
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
It has been a long standing problem to find good symbolic codings for translations on the $d$-dimensional torus that enjoy the beautiful properties of Sturmian sequences like low factor complexity and good local discrepancy properties.…
Concrete computing machines, either sequential or concurrent, rely on an intimate relation between computation and time. We recall the general characteristic properties of physical time and of present realizations of computing systems. We…
Causal models, also known as Structural Equation Models (SEM), are a well-known formalism for representing and reasoning about causal dependencies between events. In this paper, we show that Temporal SEMs (TSEMs), which extend SEMs to…
The Tsetlin Machine (TM) is a novel machine learning algorithm with several distinct properties, including transparent inference and learning using hardware-near building blocks. Although numerous papers explore the TM empirically, many of…
Ising machines are dedicated hardware solvers of NP-hard optimization problems. However, they do not always find the most optimal solution. The probability of finding this optimal solution depends on the problem at hand. Using continuation…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets, and uniformly continuous maps is presented. In work of Berger it was shown how to extract certified algorithms working with the signed…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…
Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model,…