Automaticity of Primitive Words and Irreducible Polynomials

作者：Lacroix Anne^*; Rampersad Narad

来源：Discrete Mathematics and Theoretical Computer Science, 2013, 15(1): 29-36.

• automaticity
• primitive word
• unbordered word
• irreducible polynomial

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.

• 出版日期2013