文章基本信息

标题：Nondeterministic State Complexity of Positional Addition
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作者：Galina Jirásková ; Alexander Okhotin
期刊名称：Electronic Proceedings in Theoretical Computer Science
电子版ISSN：2075-2180
出版年度：2009
卷号：3
页码：151-161
DOI：10.4204/EPTCS.3.14
出版社：Open Publishing Association
摘要：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.