Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.   provide bounds for the automaticity of the language of primitive words and the language of unbordered words over a k-letter alphabet.   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.
['Anne Lacroix', 'Narad Rampersad']
I am writing a research paper on a idea Automaticity of primitive words and irreducible polynomials
[{"from": "human", "value": "I am writing a research paper on a idea Automaticity of primitive words and irreducible polynomials"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.   provide bounds for the automaticity of the language of primitive words and the language of unbordered words over a k-letter alphabet.   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."}]