Related papers: Fast Synchronization of Random Automata
We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is…
We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to…
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…
Existing training criteria in automatic speech recognition(ASR) permit the model to freely explore more than one time alignments between the feature and label sequences. In this paper, we use entropy to measure a model's uncertainty, i.e.…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
We study ideal languages generated by a single word. We provide an algorithm to construct a strongly connected synchronizing automaton for which such a language serves as the language of synchronizing words. Also we present a compact…
Concurrent programs are notoriously hard to write correctly, as scheduling nondeterminism introduces subtle errors that are both hard to detect and to reproduce. The most common concurrency errors are (data) races, which occur when…
A system of communicating finite state machines is synchronizable if its send trace semantics, i.e.the set of sequences of sendings it can perform, is the same when its communications are FIFO asynchronous and when they are just rendez-vous…
Rapid expansions of their size and frequent changes of their topology make it difficult to observe and analyze complex networks. We explore the properties of the Hankel matrix and propose an algorithm for calculating the final…
In this work we bring out the existence of a novel kind of synchronization associated to the size of a complex system. A dichotomic random jump process associated to the dynamics of an externally driven stochastic system with $N$ coupled…
A deterministic finite-state automaton (FSA) is an abstract sequential machine that reads the symbols comprising an input word one at a time. An FSA is symmetric if its output is independent of the order in which the input symbols are read,…
For a fixed alphabet $A$, an infinite sequence $X$ is said to be normal if every word $w$ over $A$ appears in $X$ with the same frequency as any other word of the same length. A classical result of Agafonov (1966) relates normality to…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
The asynchronous automaton associated with a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ is considered in many applications. It is the finite deterministic automaton with set of states $\{0,1\}^n$, alphabet $\{1,\dots,n\}$, where the action…
Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to…
Complex systems in a wide variety of areas such as biological modeling, image processing, and language recognition can be modeled using networks of very simple machines called finite automata. Connecting subsystems modeled using finite…
An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More generally, we have morphic sequences, which are letter-to-letter codings of fixed points of arbitrary morphisms. There are many examples where…
Synchronizing sequences have been proposed in the late 60's to solve testing problems on systems modeled by finite state machines. Such sequences lead a system, seen as a black box, from an unknown current state to a known final one. This…
The results of several papers concerning the \v{C}ern\'y conjecture are deduced as consequences of a simple idea that I call the averaging trick. This idea is implicitly used in the literature, but no attempt was made to formalize the proof…
Parametric timed automata are a powerful formalism for reasoning on concurrent real-time systems with unknown or uncertain timing constants. Reducing their state space is a significant way to reduce the inherently large analysis times. We…