Abstract
Let \(\mathcal{A}=(Q,\Sigma,\delta)\) be a finite deterministic complete automaton. \(\mathcal{A}\) is called k-compressible if there is a word w ∈ Σ + such that the image of the state set Q under the action of w has at most size |Q| − k, in such case the word w is called k-compressing for \(\mathcal{A}\). A word w ∈ Σ + is k-collapsing if it is k-compressing for each k-compressible automaton of the alphabet Σ and it is k-synchronizing if it is k-compressing for each k-compressible automaton with k + 1 states (see [1,2] for details).
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References
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Cherubini, A., Frigeri, A., Piochi, B. (2011). Short 3-Collapsing Words over a 2-Letter Alphabet. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_42
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