Collapsing Words vs. Synchronizing Words
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
On the Completion of Codes in Submonoids with Finite Rank
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
An algorithm for recognition of n-collapsing words
Theoretical Computer Science
Language and Automata Theory and Applications
Collapsing words, permutation conditions and coherent colorings of trees
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
Completing a code in a regular submonoid of the free monoid
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
On the Completion of Codes in Submonoids with Finite Rank
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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A word w over a finite alphabet Σ is said to be n-collapsing if for an arbitrary finite automaton A = 〈Q,Σ_._〉, the inequality |Q ċ w| ≤ |Q|- n holds provided that |Q ċ u| ≤ |Q|- n for some word u (depending on A). We give an algorithm to test whether a word is 2-collapsing. To this aim we associate to every word w a finite family of finitely generated subgroups in finitely generated free groups and prove that the property of being 2-collapsing reflects in the property that each of these subgroups has index at most 2 in the corresponding free group. We also find a similar characterization for the closely related class of so-called 2-synchronizing words.