Abstract
A word w over a finite alphabet Σ is n-collapsing if for an arbitrary DFA \({\mathcal A}=\langle Q,\Sigma,\delta\rangle\), the inequality |δ(Q,w)| ≤ |Q| − n holds provided that |δ(Q,u)| ≤ |Q| − n for some word u∈Σ + (depending on \({\mathcal A}\)). We overview some recent results related to this notion. One of these results implies that the property of being n-collapsing is algorithmically recognizable for any given positive integer n.
The authors acknowledge support from the Federal Education Agency of Russia, grants 49123 and 04.01.437, the Russian Foundation for Basic Research, grant 05-01-00540, and the Federal Science and Innovation Agency of Russia, grant 2227.2003.01
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Ananichev, D.S., Petrov, I.V., Volkov, M.V. (2005). Collapsing Words: A Progress Report. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_2
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DOI: https://doi.org/10.1007/11505877_2
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