If L is a language, the automaticity function A_L(n) (resp. N_L(n)) of L counts the number of states of a smallest deterministic (resp. non-deterministic) finite automaton that accepts a language that agrees with L on all inputs of length at most n. We provide bounds for the automaticity of the language of primitive words and the language of unbordered words over a k-letter alphabet. We also give a bound for the automaticity of the language of base-b representations of the irreducible polynomials over a finite field. This latter result is analogous to a result of Shallit concerning the base-k representations of the set of prime numbers.

Source : oai:HAL:hal-00990604v1

Volume: Vol. 15 no. 1

Section: Automata, Logic and Semantics

Published on: January 28, 2013

Submitted on: July 4, 2011

Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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