Reset sequences for monotonic automata
SIAM Journal on Computing
Synchronizing finite automata on Eulerian digraphs
Theoretical Computer Science - Mathematical foundations of computer science
Synchronizing Automata and the Černý Conjecture
Language and Automata Theory and Applications
The Synchronization Problem for Strongly Transitive Automata
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
A Quadratic Upper Bound on the Size of a Synchronizing Word in One-Cluster Automata
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Synchronizing automata preserving a chain of partial orders
Theoretical Computer Science
Strongly transitive automata and the Černý conjecture
Acta Informatica
An efficient algorithm finds noticeable trends and examples concerning the Černy conjecture
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Composition sequences and synchronizing automata
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
The Synchronizing Probability Function of an Automaton
SIAM Journal on Discrete Mathematics
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Recently, Carpi and D'Alessandro [3] have formulated a conjecture whose validity would imply an O(n2) upper bound for the minimum length of reset words for synchronizing automata with n states. We refute this conjecture as well as a related conjecture by Rystsov [13] and suggest a weaker version that still suffices to achieve a quadratic upper bound.