Related papers: On computational irreducibility and the predictabi…
Deep convolutional neural networks have shown high efficiency in computer visions and other applications. However, with the increase in the depth of the networks, the computational complexity is growing exponentially. In this paper, we…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of…
We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction, and use it to define a notion of executable transition system. We show that every computable transition system…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…
Exploring further the properties of ITRM-recognizable reals, we provide a detailed analysis of recognizable reals and their distribution in G\"odels constructible universe L. In particular, we show that, for unresetting infinite time…
Existing causal inference (CI) models are often restricted to data with low-dimensional confounders and singleton actions. We propose an autoregressive (AR) CI framework capable of handling complex confounders and sequential actions…
Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…
This short survey of recent work in tile self-assembly discusses the use of simulation to classify and separate the computational and expressive power of self-assembly models. The journey begins with the result that there is a single…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility…
Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics on the level of invariant sets, the primary objects of interest in the classical theory of dynamical systems, is not…
Recent computational experiments have demonstrated the spontaneous emergence of self-replicating programs across universal automata, artificial chemistries, and self-modifying code systems. Remarkably, these results arise without explicit…
Active matter, responsive ("smart") materials and materials under time-dependent load are systems out of thermal equilibrium. To construct coarse-grained models for such systems, one needs to integrate out a distribution of microstates that…
We introduce infinite time computable model theory, the computable model theory arising with infinite time Turing machines, which provide infinitary notions of computability for structures built on the reals R. Much of the finite time…