Reset sequences for monotonic automata
SIAM Journal on Computing
Synchronizing automata with a letter of deficiency 2
Theoretical Computer Science
Synchronizing Automata and the Černý Conjecture
Language and Automata Theory and Applications
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Modifying the upper bound on the length of minimal synchronizing word
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Complexity of problems concerning carefully synchronizing words for PFA and directing words for NFA
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
FATES'05 Proceedings of the 5th international conference on Formal Approaches to Software Testing
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Two topics are presented: synchronization games and synchronization costs. In a synchronization game on a deterministic finite automaton, there are two players, Alice and Bob, whose moves alternate. Alice wants to synchronize the given automaton, while Bob aims to make her task as hard as possible. We answer a few natural questions related to such games. Speaking about synchronization costs, we consider deterministic automata in which each transition has a certain price. The problem is whether or not a given automaton can be synchronized within a given budget. We determine the complexity of this problem.