State Complexity of Testing Divisibility

Details State Complexity of Testing Divisibility State Complexity of Testing Divisibility

2010-08-10

arxiv.org/abs/1008.1668v1

EPTCS 31, 2010, pp. 48-57

Computer Science

Formal Languages and Automata Theory

In Proceedings DCFS 2010, arXiv:1008.1270

Scientific paper

10.4204/EPTCS.31.7

Under some mild assumptions, we study the state complexity of the trim
minimal automaton accepting the greedy representations of the multiples of m >=
2 for a wide class of linear numeration systems. As an example, the number of
states of the trim minimal automaton accepting the greedy representations of
the multiples of m in the Fibonacci system is exactly 2m^2.

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