Nondeterministic State Complexity of Positional Addition

@article{Jirskov2009NondeterministicSC,
  title={Nondeterministic State Complexity of Positional Addition},
  author={Galina Jir{\'a}skov{\'a} and Alexander Okhotin},
  journal={Journal of Automata, Languages and Combinatorics},
  year={2009},
  volume={15},
  pages={121-133}
}
Consider nondeterministic finite automata recognizing bas e-k positional notation of numbers. Assume that numbers are read starting from their least signific a t digits. It is proved that if two sets of numbersS andT are represented by nondeterministic automata of m andn states, respectively, then their sum{s + t | s ∈ S, t ∈ T } is represented by a nondeterministic automaton with 2mn+2m+2n+1 states. Moreover, this number of states is necessary in the worst case for all k > 9. 

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