Highly Influenced

3 Excerpts

@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} }

- Published in DCFS 2009
DOI:10.4204/EPTCS.3.14

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.