Related papers: On incomplete and synchronizing finite sets
A word w of letters on edges of underlying graph Gamma of deterministic finite automaton (DFA) is called the synchronizing word if w sends all states of the automaton to a unique state. J. Cerny discovered in 1964 a sequence of n-state…
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 present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\varTheta(n^2)$, where…
We approach the task of computing a carefully synchronizing word of optimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this…
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…
A word $w$ is called synchronizing (recurrent, reset, magic, directable) word of deterministic finite automaton (DFA) if $w$ sends all states of the automaton to a unique state. In 1964 Jan \v{C}erny found a sequence of n-state complete DFA…
An automaton is synchronizing if there is a word that maps all states onto the same state. \v{C}ern\'{y}'s conjecture on the length of the shortest such word is probably the most famous open problem in automata theory. We consider the…
We study extremal and algorithmic questions of subset and careful synchronization in monotonic automata. We show that several synchronization problems that are hard in general automata can be solved in polynomial time in monotonic automata,…
A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Cerny had found in 1964 a sequence of n-state complete DFA with…
In [1], we introduced the weakly synchronizing languages for probabilistic automata. In this report, we show that the emptiness problem of weakly synchronizing languages for probabilistic automata is undecidable. This implies that the…
A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state deterministic automaton has a synchronizing word, then…
We study synchronizing automata with the shortest reset words of relatively large length. First, we refine the Frankl-Pin result on the length of the shortest words of rank $m$, and the B\'eal, Berlinkov, Perrin, and Steinberg results on…
We follow language theoretic approach to synchronizing automata and \v{C}ern\'{y}'s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a…
We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability 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…
A finite set S of words over the alphabet A is called non-complete if Fact(S*) is different from A*. A word w in A* - Fact(S*) is said to be uncompletable. We present a series of non-complete sets S_k whose minimal uncompletable words have…
We study a connection between synchronizing automata and its set $M$ of minimal reset words, i.e., such that no proper factor is a reset word. We first show that any synchronizing automaton having the set of minimal reset words whose set of…
Cerny's conjecture is a longstanding open problem in automata theory. We study two different concepts, which allow to approach it from a new angle. The first one is the triple rendezvous time, i.e., the length of the shortest word mapping…
Using combinatorial properties of incomplete sets in a free monoid we construct a series of n-state deterministic automata with zero whose shortest synchronizing word has length n^2/4+n/2-1.