Combinatorics on Words pp 205-216 | Cite as
Regular Ideal Languages and Synchronizing Automata
Conference paper
Abstract
We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some strongly connected synchronizing automaton. Furthermore, this one-to-one correspondence allows us to formulate Černý’s conjecture in a pure language theoretic framework.
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References
- 1.Gusev, V., Maslennikova, M., Pribavkina, E.: Principal ideal languages and synchronizing automata. In: Halava, V., Karhumaki, J., Matiyasevich, Y. (eds.) RuFiDimII. TUCS Lecture Notes, vol. 17 (2012)Google Scholar
- 2.Gusev, V.V., Maslennikova, M.I., Pribavkina, E.V.: Finitely generated ideal languages and synchronizing automata. In: Karhumäki, J., Lepistö, A., Zamboni, L. (eds.) WORDS 2013. LNCS, vol. 8079, pp. 143–153. Springer, Heidelberg (2013)Google Scholar
- 3.Maslennikova, M.: Reset complexity of ideal languages. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Špánek, R., Turán, G. (eds.) Proc. Int. Conf. SOFSEM 2012, vol. II, pp. 33–44. Institute of Computer Science Academy of Sci- ences of the Czech Republic (2012)Google Scholar
- 4.Pin, J.E.: On two combinatorial problems arising from automata theory. Ann. Discrete Math. 17, 535–548 (1983)MATHGoogle Scholar
- 5.Pribavkina, E.V., Rodaro, E.: Finitely generated synchronizing automata. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 672–683. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 6.Pribavkina, E.V., Rodaro, E.: State complexity of prefix, suffix, bifix and infix operators on regular languages. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 376–386. Springer, Heidelberg (2010)CrossRefGoogle Scholar
- 7.Pribavkina, E.V., Rodaro, E.: Recognizing synchronizing automata with finitely many minimal synchronizing words is PSPACE-complete. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds.) CiE 2011. LNCS, vol. 6735, pp. 230–238. Springer, Heidelberg (2011)CrossRefGoogle Scholar
- 8.Pribavkina, E.V., Rodaro, E.: State complexity of code operators. International Journal of Foundations of Computer Science 22(07), 1669–1681 (2011)MathSciNetMATHCrossRefGoogle Scholar
- 9.Pribavkina, E.V., Rodaro, E.: Synchronizing automata with finitely many minimal synchronizing words. Information and Computation 209(3), 568–579 (2011), http://www.sciencedirect.com/science/article/pii/S0890540110002063 MathSciNetMATHCrossRefGoogle Scholar
- 10.Rystsov, I.: Reset words for commutative and solvable automata. Theoretical Computer Science 172(1-2), 273–279 (1997), http://www.sciencedirect.com/science/article/pii/S0304397596001363 MathSciNetMATHCrossRefGoogle Scholar
- 11.Černý, J.: Poznámka k homogénnym eksperimentom s konečnými automatami. Mat.-Fyz. Čas. Slovensk. Akad. Vied. 14, 208–216 (1964) (in slovak)MATHGoogle Scholar
- 12.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)CrossRefGoogle Scholar
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