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We survey several results and open problems related to synchronizing automata. In particular, we discuss some recent advances towards a solution of the Cerný conjecture.
We provide an overview of recent research on the natural question what makes a finite semigroup have finite or infinite identity basis. An emphasis is placed on results published since 1985 when the… (More)
We show that if the state set Q of a synchronizing automaton A = 〈Q, Σ, δ〉 admits a linear order such that for each letter a ∈ Σ the transformation δ(_,a) of Q preserves this order, then A possesses… (More)
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… (More)
A word w over a *nite alphabetis saidto be n-collapsing if for an arbitrary *nite automaton A = � Q; � −·−� , the inequality |Q · w| 6 |Q |− n holds provided that |Q · u| 6 |Q |− n for some word u… (More)
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under… (More)
Introduction.- 1. Main definitions and basic fact.- 2. Words that can be avoided.- 3. Semigroups.- 4. Rings.- 5. Groups.- Bibliography.- Index.
We show that the interval of the lattice of semigroup pseudovarieties between the pseudovarieties generated by all semigroups of full and respectively, partial, order-preserving transformations of a… (More)
In an earlier paper, we have studied reset words for synchronizing automata whose states admit a stable linear order. Here we show that the same bound on the length of the shortest reset word… (More)
We present several infinite series of synchronozing automata for which the minimum length of reset words is close to the square of the number of states. All these automata are tightly related to… (More)