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Nondeterministic State Complexity of Positional Addition

Galina Jirásková, Alexander Okhotin

2009
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Electronic Proceedings in Theoretical Computer Science
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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 ...
For every k 9, the *nondeterministic* *state* *complexity* *of* *positional* *addition* is given by the function f k (m, n) = 6, if m = n = 1, 2mn + 2m + 2n + 1, if m + n 3. ...

doi:10.4204/eptcs.3.14
fatcat:mxhc7t7fjrhzzfur254kmja3hy