Abstract
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.
Supported by the Russian Foundation for Basic Research, grant 10-01-00793.
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Ananichev, D.S., Volkov, M.V., Zaks, Y.I.: Synchronizing automata with a letter of deficiency 2. Theor. Comput. Sci. 376, 30–41 (2007)
Béal, M.-P., Perrin, D.: A quadratic algorithm for road coloring. Technical report, Université Paris-Est (2008), http://arxiv.org/abs/0803.0726
Blass, A., Gurevich, Y., Nachmanson, L., Veanes, M.: Play to Test. In: Grieskamp, W., Weise, C. (eds.) FATES 2005. LNCS, vol. 3997, pp. 32–46. Springer, Heidelberg (2006)
Černý, J.: Poznámka k homogénnym eksperimentom s konečnými automatami. Matematicko-fyzikalny Časopis Slovensk. Akad. Vied 14(3), 208–216 (1964) (in Slovak)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, McGraw-Hill, Cambridge (2009)
Eppstein, D.: Reset sequences for monotonic automata. SIAM J. Comput. 19, 500–510 (1990)
Martyugin, P.V.: Complexity of Problems Concerning Carefully Synchronizing Words for PFA and Directing Words for NFA. In: Ablayev, F., Mayr, E.W. (eds.) CSR 2010. LNCS, vol. 6072, pp. 288–302. Springer, Heidelberg (2010)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1994)
Perles, M., Rabin, M.O., Shamir, E.: The theory of definite automata. IEEE Trans. Electronic Comput. 12, 233–243 (1963)
Pin, J.-E.: On two combinatorial problems arising from automata theory. Ann. Discrete Math. 17, 535–548 (1983)
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)
Sandberg, S.: Homing and Synchronizing Sequences. In: Broy, M., Jonsson, B., Katoen, J.-P., Leucker, M., Pretschner, A. (eds.) Model-Based Testing of Reactive Systems. LNCS, vol. 3472, pp. 5–33. Springer, Heidelberg (2005)
Trahtman, A.: The Road Coloring Problem. Israel J. Math. 172(1), 51–60 (2009)
Trahtman, A.N.: Modifying the Upper Bound on the Length of Minimal Synchronizing Word. In: Owe, O., Steffen, M., Telle, J.A. (eds.) FCT 2011. LNCS, vol. 6914, pp. 173–180. Springer, Heidelberg (2011)
Volkov, M.V.: Synchronizing Automata and the Černý Conjecture. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 11–27. Springer, Heidelberg (2008)
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Fominykh, F., Volkov, M. (2012). P(l)aying for Synchronization. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_14
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