Related papers: Infinite Time Cellular Automata: A Real Computatio…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
The power of real-time Turing machines using sublinear space is investigated. In contrast to a claim appearing in the literature, such machines can accept non-regular languages, even if working in deterministic mode. While maintaining a…
As the particle count escalates, the computational demands of diverse simulation algorithms surge, paralleled by a marked enhancement in accuracy. The question arises whether this heightened precision asymptotically dwindles towards zero or…
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…
We construct a one-dimensional uniquely ergodic cellular automaton which is not nilpotent. This automaton can perform asymptotically infinitely sparse computation, which nevertheless never disappears completely. The construction builds on…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
Invertible cellular automata are useful as models of physical systems with microscopically revesible dyanmics. There are several well-understood ways to construct them: partitioning rules, second-order rules, and alternating-grid rules. We…
We present a number of new physical systems that may be addressed using methods of time dependent transformation. A recap of results available for two-state systems is given, with particular emphasis on the AC stark effect. We give some…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
We define Oracle-Type-2-Machine capable of writing infinite oracle queries. In contrast to finite oracle queries, this extends the realm of oracle-computable functions into the discontinuous realm. Our definition is conservative; access to…
The increasing importance of such fields as embedded systems, pervasive computing, and hybrid systems control is increasing attention to the time-dependent aspects of system modeling. In this paper, we focus on modeling conceptual time.…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…
In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models' hyperparameters, the proposed algorithm particularly solves…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hypothesis tests for time series models require nuanced…
A wide family of nonlinear sequence generators, the so-called clock-controlled shrinking generators, has been analyzed and identified with a subset of linear cellular automata. The algorithm that converts the given generator into a linear…
This article surveys some theoretical aspects of Cellular Automata (CAs) research. In particular, we discuss on maximal length CA. An n-cell CA is a maximal length CA, if all the configurations except one form a single cycle. There is a…