The Černý Conjecture for Aperiodic Automata
A word w is called a synchronizing (recurrent, reset, directable) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some specific state; a DFA that has a synchronizing word is said to be synchronizable. Cerny conjectured in 1964 that every n-state synchro...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2007-05-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/649 |
| _version_ | 1818120329978970112 |
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| author | Avraham N. Trahtman |
| author_facet | Avraham N. Trahtman |
| author_sort | Avraham N. Trahtman |
| collection | DOAJ |
| description | A word w is called a synchronizing (recurrent, reset, directable) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some specific state; a DFA that has a synchronizing word is said to be synchronizable. Cerny conjectured in 1964 that every n-state synchronizable DFA possesses a synchronizing word of length at most (n-1) 2. We consider automata with aperiodic transition monoid (such automata are called aperiodic). We show that every synchronizable n-state aperiodic DFA has a synchronizing word of length at most n(n-1)/2. Thus, for aperiodic automata as well as for automata accepting only star-free languages, the Cerny conjecture holds true. |
| first_indexed | 2024-12-11T05:24:22Z |
| format | Article |
| id | doaj.art-97835fff9cde4b81909010e1147a4f69 |
| institution | Directory Open Access Journal |
| issn | 1462-7264 1365-8050 |
| language | English |
| last_indexed | 2024-12-11T05:24:22Z |
| publishDate | 2007-05-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-97835fff9cde4b81909010e1147a4f692022-12-22T01:19:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502007-05-0192The Černý Conjecture for Aperiodic AutomataAvraham N. TrahtmanA word w is called a synchronizing (recurrent, reset, directable) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some specific state; a DFA that has a synchronizing word is said to be synchronizable. Cerny conjectured in 1964 that every n-state synchronizable DFA possesses a synchronizing word of length at most (n-1) 2. We consider automata with aperiodic transition monoid (such automata are called aperiodic). We show that every synchronizable n-state aperiodic DFA has a synchronizing word of length at most n(n-1)/2. Thus, for aperiodic automata as well as for automata accepting only star-free languages, the Cerny conjecture holds true.http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/649 |
| spellingShingle | Avraham N. Trahtman The Černý Conjecture for Aperiodic Automata Discrete Mathematics & Theoretical Computer Science |
| title | The Černý Conjecture for Aperiodic Automata |
| title_full | The Černý Conjecture for Aperiodic Automata |
| title_fullStr | The Černý Conjecture for Aperiodic Automata |
| title_full_unstemmed | The Černý Conjecture for Aperiodic Automata |
| title_short | The Černý Conjecture for Aperiodic Automata |
| title_sort | cerny conjecture for aperiodic automata |
| url | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/649 |
| work_keys_str_mv | AT avrahamntrahtman thecernyconjectureforaperiodicautomata AT avrahamntrahtman cernyconjectureforaperiodicautomata |