Abstract
We prove that the tight bound on the state complexity of the boundary of regular languages, defined as bd\((L)=L^* \cap ( \, \overline{L} \, )^*\), is 22n − 2 + 22n − 3 + 2n − 2 + 2 − 2·3n − 2 − n. Our witness languages are described over a five-letter alphabet. For a four-letter alphabet, the lower bound is smaller by just one, and we conjecture that the upper bound cannot be met in the quaternary case.
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Jirásek, J., Jirásková, G. (2013). On the Boundary of Regular Languages. In: Konstantinidis, S. (eds) Implementation and Application of Automata. CIAA 2013. Lecture Notes in Computer Science, vol 7982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39274-0_19
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DOI: https://doi.org/10.1007/978-3-642-39274-0_19
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