Geodesic
The mirror image of the language of 2-synchronizing words
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2010), pp. 69-73.

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A word $w$ over a finite alphabet $\Sigma$ is called $n$-synchronizing if for each deterministic finite automaton $\mathscr A=\langle Q,\Sigma,\delta\rangle$ such that $|Q|=n+1$ the equality $|\delta(Q,w)|=1$ holds provided that $|\delta(Q,u)|=1$ for some word $u\in\Sigma^*$ (depending on $\mathscr A$). In this paper we prove that the language of all 2-synchronizing words is closed under the mapping that associates each word $w=a_1a_2\cdots a_t\in\Sigma^*$ with its mirror image $\overleftarrow w=a_t\cdots a_2a_1$.
Keywords: synchronizing word, universal synchronizing word, synchronizable automaton, mirror image, formal language. 
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2010_1_a6/}
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I. V. Petrov. The mirror image of the language of 2-synchronizing words. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2010), pp. 69-73. http://geodesic.mathdoc.fr/item/IVM_2010_1_a6/

[1] Ananichev D. S., Volkov M. V., “Collapsing words vs. synchronizing words”, Lect. Notes Comp. Sci., 2295, 2002, 166–174 | MR | Zbl

[2] Ananichev D. S., Petrov I. V, “Quest for short synchronizing words and short collapsing words”, TUCS Gen. Publ., 27, Turku Centre of Computer Science, Turku, 2003, 411–418 | MR | Zbl