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On Polynomial Recursive Sequences.

Michaël Cadilhac1, Filip Mazowiecki2, Charles Paperman3

  • 1DePaul University, Chicago, IL 60484 USA.

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PubMed
Summary
This summary is machine-generated.

We investigated polynomial recursive sequences, a nonlinear extension of linear ones. Our key finding is that the sequence n^2 is not polynomial recursive, impacting the study of nonlinear weighted automata.

Keywords:
Expressive powerHigher-order pushdown automataRecursive sequencesWeighted automata

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Area of Science:

  • Theoretical computer science
  • Formal languages and automata theory

Background:

  • Polynomial recursive sequences are a nonlinear extension of linear recursive sequences.
  • These sequences are relevant to nonlinear weighted automata and class separations.
  • A known example of a polynomial recursive sequence is n!

Purpose of the Study:

  • To determine the expressive power of polynomial recursive sequences.
  • To investigate the expressiveness of the sequence n^2 within this framework.

Main Methods:

  • Analysis of the properties of polynomial recursive sequences.
  • Demonstration of the non-expressiveness of n^2 using theoretical methods.

Main Results:

  • The sequence n^2 is proven to not be polynomial recursive.
  • This result contributes to understanding the limitations of polynomial recursive sequences.

Conclusions:

  • The class of polynomial recursive sequences has limitations in expressive power.
  • The findings have implications for the study of nonlinear weighted automata and their separations.