Related papers: An Extremal Series of Eulerian Synchronizing Autom…
It is shown that, for every $n \geqslant 2$, the maximum length of the shortest string accepted by an $n$-state direction-determinate two-way finite automaton is exactly $\binom{n}{\lfloor\frac{n}{2}\rfloor}-1$ (direction-determinate…
We present a strongly exponential lower bound that applies both to the subset synchronization threshold for binary deterministic automata and to the careful synchronization threshold for binary partial automata. In the later form, the…
In a recent article by Chapuy and Perarnau, it was shown that a uniformly chosen automaton on $n$ states with a $2$-letter alphabet has a synchronizing word of length $O(\sqrt{n}\log n)$ with high probability. In this note, we improve this…
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…
A word w is called a synchronizing (recurrent, reset) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some state; a DFA that has a synchronizing word is said to be synchronizing. Cerny conjectured…
We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. $\textit{Complement:}$ There is a language $L$ recognised by an $n$-state UFA such…
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…
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,…
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…
We examine the reset threshold of randomly generated deterministic automata. We present a simple proof that an automaton with a random mapping and two random permutation letters has a reset threshold of $\mathcal{O}\big( \sqrt{n \log^3 n}…
This paper situates itself in the theory of variable length codes and of finite automata where the concepts of completeness and synchronization play a central role. In this theoretical setting, we investigate the problem of finding upper…
This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…
In this paper, we first introduce a lower bound technique for the state complexity of transformations of automata. Namely we suggest first considering the class of full automata in lower bound analysis, and later reducing the size of the…
The set of synchronizing words of a given $n$-state automaton forms a regular language recognizable by an automaton with $2^n - n$ states. The size of a recognizing automaton for the set of synchronizing words is linked to computational…
It is proved that every regular expression of alphabetic width $n$, that is, with $n$ occurrences of symbols of the alphabet, can be transformed into a deterministic finite automaton (DFA) with $2^{\frac{n}{2}+(\frac{\log_2…
While the complexity of translating future linear temporal logic (LTL) into automata on infinite words is well-understood, the size increase involved in turning automata back to LTL is not. In particular, there is no known elementary bound…
Motivated by the Babai conjecture and the Cerny conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with $n$ states in this class, we…
We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This…
We consider the following problem: given that a finite automaton $M$ of $N$ states accepts at least one $k$-power-free (resp., overlap-free) word, what is the length of the shortest such word accepted? We give upper and lower bounds which,…
A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration.…