Related papers: Testing a cellular automata construction method to…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…
A quantum single-error-correcting scheme can be derived from a one-way entanglement purification protocol in purifying one Bell state from a finite block of five Bell states. The main issue to be concerned with in the theory of such an…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in…
We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the…
We present a constructive method to create quantum circuits that implement oracles $|x\rangle|y\rangle|0\rangle^k \mapsto |x\rangle|y \oplus f(x)\rangle|0\rangle^k$ for $n$-variable Boolean functions $f$ with low $T$-count. In our method…
The increasing complexity of control systems necessitates control laws that guarantee safety w.r.t. complex combinations of constraints. In this letter, we propose a framework to describe compositional safety specifications with control…
Boolean functions are important primitives in different domains of cryptology, complexity and coding theory. In this paper, we connect the tools from cryptology and complexity theory in the domain of Boolean functions with low polynomial…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
A probabilistic cellular automaton (PCA) can be viewed as a Markov chain. The cells are updated synchronously and independently, according to a distribution depending on a finite neighborhood. We investigate the ergodicity of this Markov…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
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…
Physical Unclonable Functions evaluate manufacturing variations to generate secure cryptographic keys for embedded systems without secure key storage. It is explained how methods from coding theory are applied in order to ensure reliable…
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…
We exhibit a Probabilistic Cellular Automaton (PCA) on the integers with an alphabet and a neighborhood of size 2 which is non-ergodic although it has a unique invariant measure. This answers by the negative an old open question on whether…
The execution of sequential programs allows them to be represented using mathematical functions formed by the composition of statements following one after the other. Each such statement is in itself a partial function, which allows only…
The use of buried dopants to construct quantum-dot cellular automata is investigated as an alternative to conventional electronic devices for information transport and elementary computation. This provides a limit in terms of…
This paper investigates the $k$-mixing property of a multidimensional cellular automaton. Suppose $F$ is a cellular automaton with the local rule $f$ defined on a $d$-dimensional convex hull $\mathcal{C}$ which is generated by an apex set…
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…