Reset sequences for monotonic automata
SIAM Journal on Computing
Introduction to Linear Optimization
Introduction to Linear Optimization
Synchronizing finite automata on Eulerian digraphs
Theoretical Computer Science - Mathematical foundations of computer science
Convex Optimization
Synchronizing generalized monotonic automata
Theoretical Computer Science - Insightful theory
Synchronizing Automata and the Černý Conjecture
Language and Automata Theory and Applications
The Synchronization Problem for Locally Strongly Transitive Automata
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
On a conjecture by Carpi and D'Alessandro
DLT'10 Proceedings of the 14th international conference on Developments in language theory
The averaging trick and the Černý conjecture
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Modifying the upper bound on the length of minimal synchronizing word
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Approximating the minimum length of synchronizing words is hard
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Synchronizing automata on quasi-eulerian digraph
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
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We study the synchronization phenomenon for deterministic finite state automata and the related longstanding Černý conjecture. We formulate this conjecture in the setting of a two-player probabilistic game. Our goal is twofold. On the one hand, the probabilistic interpretation is of interest in its own right and can be applied to real-world situations. On the other hand, our formulation makes use of standard convex optimization techniques, which appear powerful to shed light on Černý's conjecture. We analyze the synchronization phenomenon through this particular point of view. Among other properties, we prove that the synchronization process cannot stagnate too long in a certain sense. We propose a new conjecture and demonstrate that its validity would imply Černý's conjecture. We show numerical evidence for the pertinence of the approach.