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.
@article{IVM_2010_1_a6,
author = {I. V. Petrov},
title = {The mirror image of the language of 2-synchronizing words},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {69--73},
publisher = {mathdoc},
number = {1},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2010_1_a6/}
}
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/