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We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…
In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…
In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the…
This paper proposes several algorithms and their Cellular Automata Machine (CAM) for drawing the State Transition Diagram (STD) of an arbitrary Cellular Automata (CA) Rule (any neighborhood, uniform/ hybrid and null/ periodic boundary) and…
In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite-state automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it.…
Most slowly synchronizing automata over binary alphabets are circular, i.e., containing a letter permuting the states in a single cycle, and their set of synchronizing words has maximal state complexity, which also implies complete…
The synthesis of reactive systems aims for the automated construction of strategies for systems that interact with their environment. Whereas the synthesis approach has the potential to change the development of reactive systems…
The conventional spin dynamics simulations are performed in direct products of state spaces of individual spins. In a general system of n spins, the total number of elements in the state basis is >4^n. A system propagation step requires an…
Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing infinite-state systems in which states are represented by terms, and sets of states by Tree Automata (TA). The central problem in TRMC is to decide…
The state complexity of a finite(-state) automaton intuitively measures the size of the description of the automaton. Sakoda and Sipser [STOC 1972, pp. 275--286] were concerned with nonuniform families of finite automata and they discussed…
Existing approaches to the synthesis of reactive systems typically involve the construction of transition systems such as Mealy automata. However, in order to obtain a succinct representation of the desired system, structured programs can…
Harnessing the intrinsic dynamics of physical systems for information processing opens new avenues for computation embodied in matter. Using simulations of a model system, we show that assemblies of DNA tiles capable of self-organizing into…
Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…
Every automaton can be decomposed into a cascade of basic prime automata. This is the Prime Decomposition Theorem by Krohn and Rhodes. Guided by this theory, we propose automata cascades as a structured, modular, way to describe automata as…
We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method…
A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
We consider the problem of reconfiguring a two-dimensional connected grid arrangement of passive building blocks from a start configuration to a goal configuration, using a single active robot that can move on the tiles, remove individual…