Image reducing words and subgroups of free groups
Theoretical Computer Science - WORDS
An algorithm for recognition of n-collapsing words
Theoretical Computer Science
An inverse automata algorithm for recognizing 2-collapsing words
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Collapsing words: a progress report
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
On some properties of the language of 2-collapsing words
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
A combinatorial approach to collapsing words
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
| Hi-index | 5.24 |
Given a word w over a finite alphabet @S and a finite deterministic automaton A=, the inequality |@d(Q,w)|@?|Q|-n means that under the natural action of the word w the image of the state set Q is reduced by at least n states. A word w is n-collapsing if this inequality holds for any deterministic finite automaton that satisfies such an inequality for at least one word. In this paper we prove that the problem of recognizing n-collapsing words is generally co-NP-complete, while restricted to 2-collapsing words over 2-element alphabet it belongs to P. This is connected with introducing a new approach to collapsing words, which is shown to be much more effective in solving various problems in the area. It leads to interesting connections with combinatorial problems concerning solving systems of permutation conditions on one hand, and coloring trees with distinguished nodes on the other hand.