Nondeterministic State Complexity of Positional Addition

Galina Jirásková, Alexander Okhotin
<span title="2009-07-30">2009</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits. It is proved that if two sets of numbers S and T are represented by nondeterministic automata of m and n states, respectively, then their sum s+t | s in S, t in 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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