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State Complexity of Multiple Catenations

Caron P., Luque J.-G., Patrou B.

Fundamenta Informaticae

2018

Vol. 160, nr 3

255--279

We improve some results relative to the state complexity of the multiple catenations described by Gao and Yu. In particular we nearly divide by 2 the size of the alphabet needed for witnesses. We also give some refinements to the algebraic expression of the state complexity, which is especially complex with this operation. We obtain these results by using peculiar DFAs defined by Brzozowski.