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A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic…
This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton's transition function. These behavioral metrics are formulated to satisfy…
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…
The density classification task is a famous problem in the theory of cellular automata. It is unsolvable for deterministic automata, but recently solutions for stochastic cellular automata have been found. One of them is a set of stochastic…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
Since their inception at {\it Macy conferences} in later 1940s complex systems remain the most controversial topic of inter-disciplinary sciences. The term `complex system' is the most vague and liberally used scientific term. Using…
In this dissertation, we study two of the global properties of 1-dimensional cellular automata (CAs) under periodic boundary condition, namely, reversibility and randomness. To address reversibility of finite CAs, we develop a mathematical…
The search for extraterrestrial life in the Solar System and beyond is a key science driver in astrobiology, planetary science, and astrophysics. A critical step is the identification and characterization of potential habitats, both to…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
The astrobiology is an interdisciplinary science, combining the methods and the means of physics, biology, chemistry and astronomy. Its main purpose is to find out if the exoplanets are habitable and if so, to confirm life on them. The…
We develop a rather elaborate computer program to investigate the jointly periodic points of one-dimensional cellular automata. The experimental results and mathematical context lead to questions, conjectures and a contextual theorem.
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…
Stochastic systems in biology often exhibit substantial variability within and between cells. This variability, as well as having dramatic functional consequences, provides information about the underlying details of the system's behaviour.…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
Timed automata are the formal model for real-time systems. Extensions with discrete probabilistic branching have been considered in the literature and successfully applied. Probabilistic timed automata (PTA) do require all branching…
Observations are an essential component of the simulation based studies on artificial-evolutionary systems (AES) by which entities are identified and their behavior is observed to uncover higher-level "emergent" phenomena. Because of the…
We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…