Related papers: Testing for Synchronization
In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the…
Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…
The work presents some new algorithms realized recently in the package TESTAS. They decide whether or not deterministic finite automaton (DFA) is synchronizing, several procedures find relatively short synchronizing words and a…
A communicating system is $k$-synchronizable if all of the message sequence charts representing the executions can be divided into slices of $k$ sends followed by $k$ receptions. It was previously shown that, for a fixed given $k$, one…
We prove that a uniformly random automaton with $n$ states on a 2-letter alphabet has a synchronizing word of length $O(n^{1/2}\log n)$ with high probability (w.h.p.). That is to say, w.h.p. there exists a word $\omega$ of such length, and…
We present a family of automata networks that solve the k-parity problem when run in parallel. These solutions are constructed by connecting cliques in a non-cyclical fashion. The size of the local neighbourhood is linear in the size of the…
The classical pattern matching paradigm is that of seeking occurrences of one string - the pattern, in another - the text, where both strings are drawn from an alphabet set $\Sigma$. Assuming the text length is $n$ and the pattern length is…
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…
In this paper we prove that a uniformly distributed random circular automaton $\mathcal{A}_n$ of order $n$ synchronizes with high probability (whp). More precisely, we prove that $$ \mathbb{P}\left[\mathcal{A}_n \text{ synchronizes}\right]…
The synchronization problem is investigated for the class of locally strongly transitive automata introduced in a previous work of the authors. Some extensions of this problem related to the notions of stable set and word of minimal rank of…
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…
A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. \v{C}ern\'y conjectured in 1964 that a synchronizing automaton with $n$ states has a synchronizing word of…
We have improved an algorithm generating synchronizing automata with a large length of the shortest reset words. This has been done by refining some known results concerning bounds on the reset length. Our improvements make possible to…
Synchronization of coupled continuous-time linear systems is studied in a general setting. For identical neutrally-stable linear systems that are detectable from their outputs, it is shown that a linear output feedback law exists under…
State minimization is a fundamental problem in automata theory. The problem is also of great importance in the study of fuzzy automata. However, most work in the literature considered only state reduction of fuzzy automata, whereas the…
Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is…
Consider a complete communication network on $n$ nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require…
In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in…
Time synchronization is a critical task in robotic computing such as autonomous driving. In the past few years, as we developed advanced robotic applications, our synchronization system has evolved as well. In this paper, we first introduce…
Instead of looking at the lengths of synchronizing words as in \v{C}ern\'y's conjecture, we look at the switch count of such words, that is, we only count the switches from one letter to another. Where the synchronizing words of the…