Nondeterministic State Complexity of Positional Addition

Galina Jirásková
(Slovak Academy of Sciences)
Alexander Okhotin
(University of Turku)

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.

In Jürgen Dassow, Giovanni Pighizzini and Bianca Truthe: Proceedings Eleventh International Workshop on Descriptional Complexity of Formal Systems (DCFS 2009), Magdeburg, Germany, July 6-9, 2009, Electronic Proceedings in Theoretical Computer Science 3, pp. 151–161.
Published: 30th July 2009.

ArXived at: bibtex PDF

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