P(l)aying for Synchronization
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.
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- 2.Béal, M.-P., Perrin, D.: A quadratic algorithm for road coloring. Technical report, Université Paris-Est (2008), http://arxiv.org/abs/0803.0726
- 8.Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1994)Google Scholar
- 11.Rystsov, I.K.: On minimizing length of synchronizing words for finite automata. In: Theory of Designing of Computing Systems, pp. 75–82. Institute of Cybernetics of Ukrainian Acad. Sci. (1980) (in Russian)Google Scholar