Abstract
We study possible deterministic state complexities of languages obtained as the Kleene star of a unary language with state complexity n. We prove that for every n, depending on the parity of n, only 3 or 4 complexities from n 2 − 4n + 6 to n 2 − 2n + 2 are attainable. On the other hand, we show that all the complexities from 1 to n are attainable. In the end, we outline a connection to the Frobenius problem.
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Čevorová, K. (2013). Kleene Star on Unary Regular Languages. In: Jurgensen, H., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2013. Lecture Notes in Computer Science, vol 8031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39310-5_26
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DOI: https://doi.org/10.1007/978-3-642-39310-5_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39309-9
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