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We start with comparisons of hierarchies in Biology and relate it to Quan- tum Field Theories. Thereby we discover many similarities and translate them into rich mathematical correspondences. The basic connection goes via scale…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
Our understanding of the Universe breaks down for very small spacetime intervals, corresponding to an extremely high level of granularity (and energy), commonly referred to as the ``Planck scale''. At this fundamental level, there are…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
In this work a collective of interacting stateless automata in a discrete geometric $n$-dimenstional environment is considered as an integral automaton-like computational dynamic object. For such distributed on the environment object…
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…
Every automaton can be decomposed into a cascade of basic prime automata. This is the Prime Decomposition Theorem by Krohn and Rhodes. Guided by this theory, we propose automata cascades as a structured, modular, way to describe automata as…
The machinery is suggested to describe the varying spacetime topology on the level of its substitutes by finite topological spaces.
In this paper we adopt a category-theoretic approach to the conception of automata classes enjoying minimization by design. The main instantiation of our construction is a new class of automata that are hybrid between deterministic automata…
We propose a method of classifying the operation of a system into finitely many modes. Each mode has its own objectives for the system's behaviour and its own mathematical models and algorithms designed to accomplish its objectives. A…
The goal of the paper is to automatize the selection of mechanisms which are able to describe a set of measurements. In order to do so first we construct a set of possible mechanism fulfilling chemically reasonable requirements with a given…
Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
We consider transformations between attractor basins of binary cylindrical cellular automata resulting from mutations. A t-point mutation of a state consists in toggling t sites in that state. Results of such mutations are described by a…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract…
We introduce the notions of topological entropy of a formal language and of a topological automaton. We show that the entropy function is surjective and bound the entropy of languages accepted by deterministic {\epsilon}-free push-down…