On the Length of Shortest 2-Collapsing Words.
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| Title: | On the Length of Shortest 2-Collapsing Words. |
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| Authors: | Cherubini, Alessandra1 alessandra.cherubini@polimi.it, Kisielewicz, Andrzej2 kisiel@math.uni.wroc.pl, Piochi, Brunetto3 piochi@math.unifi.it |
| Source: | Discrete Mathematics & Theoretical Computer Science (DMTCS). Jun2009, Vol. 11 Issue 1, p33-44. 12p. |
| Subjects: | Sequential machine theory, Vocabulary, Alphabet, Machine theory, Algorithms |
| Abstract: | Given a word w over a finite alphabet ∑ and a finite deterministic automaton A = (Q, ∑, δ), the inequality δ(Q, w))| ≤ |Q|- k means that under the natural action of the word w the image of the state set Q is reduced by at least k states. The word w is k-collapsing (k-synchronizing) if this inequality holds for any deterministic finite automaton (with k + 1 states) that satisfies such an inequality for at least one word. We prove that for each alphabet ∑ there is a 2-collapsing word whose length is |∑|³+6|∑|²+5|∑|/2 . Then we produce shorter 2-collapsing and 2-synchronizing words over alphabets of 4 and 5 letters. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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