Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   A generalization of numeration systems in which   N   is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language.  show that if   P∈  Q  [x]   is a polynomial such that   P(  N  )⊂  N   then there exists a numeration system in which the set of representations of   P(  N  )   is regular. The main issue is to construct a regular language with a complexity function equals to  P ( n +1)− P ( n ) for  n  large enough.
['Michel Rigo']
I am writing a research paper on a idea Construction of regular languages and recognizability of polynomials
[{"from": "human", "value": "I am writing a research paper on a idea Construction of regular languages and recognizability of polynomials"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   A generalization of numeration systems in which   N   is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language.  show that if   P\u2208  Q  [x]   is a polynomial such that   P(  N  )\u2282  N   then there exists a numeration system in which the set of representations of   P(  N  )   is regular. The main issue is to construct a regular language with a complexity function equals to  P ( n +1)\u2212 P ( n ) for  n  large enough."}]