Related papers: Representation of (Left) Ideal Regular Languages b…
We present a new characteristic of a regular ideal language called reset complexity. We find some bounds on the reset complexity in terms of the state complexity of a given language. We also compare the reset complexity and the state…
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…
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…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
We survey results in the literature that establish the \v{C}ern\'y conjecture for various classes of finite automata. We also list classes for which the conjecture remains open, but a quadratic (in the number of states) upper bound on the…
A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language 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…
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 refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset…
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 present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.
We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean…
Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine…
The state complexity of a regular language is the number of states in the minimal deterministic automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic…
The state complexity of a regular language is the number of states in a minimal deterministic finite automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The…
We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2^n states, where n is the maximal length of words…
We present a report from a series of experiments involving computation of the shortest reset words for automata with small number of states. We confirm that the \v{C}ern\'{y} conjecture is true for all automata with at most 11 states on 2…
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…
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.…
A right ideal is a language L over an alphabet A that satisfies L = LA*. We show that there exists a stream (sequence) (R_n : n \ge 3) of regular right ideal languages, where R_n has n left quotients and is most complex under the following…