Related papers: Reversible Causal Graph Dynamics
Causal graphs are widely used in software engineering to document and explore causal relationships. Though widely used, they may also be wildly misleading. Causal structures generated from SE data can be highly variable. This instability is…
In the mathematical tradition, reversibility requires that the evolution of a dynamical system be a bijective function. In the context of graph rewriting, however, the evolution is not even a function, because it is not even deterministic…
Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently…
Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…
We focus on a family of one-dimensional probabilistic cellular automata with memory two: the dynamics is such that the value of a given cell at time $t+1$ is drawn according to a distribution which is a function of the states of its two…
While one-dimensional cellular automata have been well studied, there are relatively few results about multidimensional cellular automata; the investigation of cellular automata defined on Cayley trees constitutes an intermediate class.…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…
A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.
Why does time appear to pass irreversibly? To investigate, we introduce a class of partitioned cellular automata (PCAs) whose cellwise evolution is based on the chaotic baker's map. After imposing a suitable initial condition and…
Causal DAGs(Directed Acyclic Graphs) are usually considered in a 2D plane. Edges indicate causal effects' directions and imply their corresponding time-passings. Due to the natural restriction of statistical models, effect estimation is…
Let $\mathbf{\Gamma} = (V,E)$ be a (non-trivial) finite graph with $\lambda: E \rightarrow \mathbb{R}_{+}$, an edge labelling of $\mathbf{\Gamma}$. Let $\rho : V\rightarrow \mathbb{R}^{2}$ be a map which preserves the edge labelling. The…
Irreversibility and acausality of a sub-system are established in exactly soluble harmonic models with reversible and causal dynamics. It is shown that initial conditions, imposed on some dynamical degrees of freedom may break time reversal…
We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over $Z_2$). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which…
Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a…
Relation between global transition function and local transition function of a homogeneous one dimensional cellular automaton (CA) is investigated for some standard transition functions. It could be shown that left shift and right shift CA…
Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…