Abstract
Given a word w over a finite alphabet Σ and a finite deterministic automaton \({\mathcal A} = {\langle} Q,\Sigma,\delta {\rangle}\), the inequality |δ(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. The 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 present a new approach to the topic of collapsing words, and announce a few results we have obtained using this new approach. In particular, we present a direct proof of the fact that the language of n-collapsing words is recursive.
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Cherubini, A., Gawrychowski, P., Kisielewicz, A., Piochi, B. (2006). A Combinatorial Approach to Collapsing Words. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_23
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DOI: https://doi.org/10.1007/11821069_23
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