50 research outputs found
The averaging trick and the Cerny conjecture
The results of several papers concerning the \v{C}ern\'y conjecture are
deduced as consequences of a simple idea that I call the averaging trick. This
idea is implicitly used in the literature, but no attempt was made to formalize
the proof scheme axiomatically. Instead, authors axiomatized classes of
automata to which it applies
Strongly transitive automata and the Cerny conjecture
The synchronization problem is investigated for a new class of deterministic automata called strongly transitive. An extension to unambiguous automata is also considered
Syntactic Complexity of Circular Semi-Flower Automata
We investigate the syntactic complexity of certain types of finitely
generated submonoids of a free monoid. In fact, we consider those submonoids
which are accepted by circular semi-flower automata (CSFA). Here, we show that
the syntactic complexity of CSFA with at most one `branch point going in' (bpi)
is linear. Further, we prove that the syntactic complexity of -state CSFA
with two bpis over a binary alphabet is
A quadratic upper bound on the size of a synchronizing word in one-cluster automata
International audienceČerný's conjecture asserts the existence of a synchronizing word of length at most (n-1)² for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p*ar = q*as for some integers r, s (for a state p and a word w, we denote by p*w the state reached from p by the path labeled w). As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n²). This applies in particular to Huffman codes