Related papers: Synchronizing Random Almost-Group Automata
We study the almost sure convergence of randomly truncated stochastic algorithms. We present a new convergence theorem which extends the already known results by making vanish the classical condition on the noise terms. The aim of this work…
This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text…
A transformation monoid on a set Omega is called synchronizing if it contains an element of rank 1 (that is, mapping the whole of Omega to a single point). In this paper, I tackle the question: given n and k, what is the probability that…
We construct a probabilistic finite automaton (PFA) with 7 states and an input alphabet of 5 symbols for which the PFA Emptiness Problem is undecidable. The only input for the decision problem is the starting distribution. For the proof, we…
We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally…
This paper deals with the size complexity of minimal {\it two-way quantum finite automata} (2qfa's) necessary for operations to perform on all inputs of each fixed length. Such a complexity measure, known as state complexity of operations,…
It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all…
A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured…
We study a variant of the synchronization game on finite deterministic automata. In this game, Alice chooses one input letter of an automaton $A$ on each of her moves while Bob may respond with an arbitrary finite word over the input…
Let G be a finite group. Let pi be a permutation from S{n}. We study the distribution of probabilities of equality a{1} a{2} ...a{n-1}a{n}=a{pi{1}}^{epsilon{1}} a{pi_{2}}^{epsilon{2}}...a{pi{n-1}}^{epsilon_{n-1}} a_{pi_{n}}^{epsilon{n}},…
We study the class of groups generated by automata that act essentially freely on the boundary of a rooted tree. In the process we establish and discuss some general tools for determining if a group belongs to this class, and explore the…
The homogeneous Kuramoto model on a graph $G = (V,E)$ is a network of $|V|$ identical oscillators, one at each vertex, where every oscillator is coupled bidirectionally (with unit strength) to its neighbors in the graph. A graph $G$ is said…
Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under…
Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the…
Algorithms for (nondeterministic) finite-state tree automata (FTAs) are often tested on random FTAs, in which all internal transitions are equiprobable. The run-time results obtained in this manner are usually overly optimistic as most such…
Small world networks interpolate between fully regular and fully random topologies and simultaneously exhibit large local clustering as well as short average path length. Small world topology has therefore been suggested to support network…
We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…
We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov…
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…