A. N. Trahtman. Notable trends concerning the synchronization of graphs and automata


Natural Sciences / Computer Science / Automata theory

Submitted on: Apr 01, 2012, 21:05:16

Description: A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Cerny had found in 1964 a sequence of n-state complete DFA with shortest synchronizing word of length (n-1)^2. He had conjectured that it is an upper bound for the length of the shortest synchronizing word for any n-state complete DFA. The examples of DFA with shortest synchronizing word of length (n-1)^2 are relatively rare. To the Cerny sequence were added in all examples of Cerny, Piricka and Rosenauerova (1971), of Kari (2001) and of Roman (2004). By help of a program based on some effective algorithms, a wide class of automata of size less than 11 was checked.

The abstract of this article has been published in the "Intellectual Archive Bulletin" , April 2012, ISSN 1929-1329.

The Library of Congress (USA) reference page : http://lccn.loc.gov/2012210064.
The Library and Archives Canada reference page: collectionscanada.gc.ca/ourl/res.php?url_ver=Z39.88......

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A_N_Trahtman_the_synchronization_of_graphs_and_automata.pdf



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