Nondeterministic State Complexity of Positional Addition
Formal Languages and Automata Theory
2009-07-30 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0907.5072,
title = {Nondeterministic State Complexity of Positional Addition},
author = {Galina Jirásková and Alexander Okhotin},
journal= {arXiv preprint arXiv:0907.5072},
year = {2009}
}