On the Difference Problem for Semilinear Power Series

We prove in this paper that if r and s are two semilinear power series in commuting variables and s has bounded coefficients, then r-s is a rational series. This result can be thought of as extending a result of Eilenberg for series in noncommuting variables. However, our proof is combinatorial, avoiding the use of a deeply algebraic cross-section theorem as in the noncommutative case.

• Type: Conference
• Year: 2003
• Where: BIRTHDAY
• Authors: Ion Petre
• Keywords: Algebraic Cross-section Theorem, Applied Computing, BIRTHDAY 2003, Rational Series, Semilinear Power Series