Related papers: A Nondeterministic Model for Abstract Geometrical …
In classical mechanics, performing a measurement without reading the measurement outcome is equivalent to not exploiting the measurement at all. A non-selective measurement in the classical realm carries no information. Here we show that…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
In the paper, we study behavior of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behavior of the system w.r.t. variety of word transformations performed by the system:…
Space is a circuit oriented, spatial programming language designed to exploit the massive parallelism available in a novel formal model of computation called the Synchronic A-Ram, and physically related FPGA and reconfigurable…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
We explore the notion of history-determinism in the context of timed automata (TA) over infinite timed words. History-deterministic (HD) automata are those in which nondeterminism can be resolved on the fly, based on the run constructed…
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…
We introduce a novel framework of reservoir computing, that is capable of both connectionist machine intelligence and symbolic computation. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous…
Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a…
The human brain has many remarkable information processing characteristics that deeply puzzle scientists and engineers. Among the most important and the most intriguing of these characteristics are the brain's broad universality as a…
We study three levels in a hierarchy of nondeterminism: A nondeterministic automaton $\mathcal{A}$ is determinizable by pruning (DBP) if we can obtain a deterministic automaton equivalent to $\mathcal{A}$ by removing some of its…
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…
Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there does not often exist a good model on the whole…
Mechanical learning is a computing system that is based on a set of simple and fixed rules, and can learn from incoming data. A learning machine is a system that realizes mechanical learning. Importantly, we emphasis that it is based on a…
This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all…
Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a…
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of…
Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of…