# Absolute Convergence - Explore the Science & Experts | ideXlab

## Absolute Convergence

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### Francois Denis – One of the best experts on this subject based on the ideXlab platform.

• ##### AbsoluteConvergence of rational series is semi decidable
Information & Computation, 2011
Co-Authors: Raphael Bailly, Francois Denis

Abstract:

This paper deals with Absolute Convergence of real-valued rational series, i.e. mappings r:Σ∗→R computed by weighted automata. An algorithm is provided, that takes a weighted automaton A as input and halts if and only if the corresponding series rA is Absolutely convergent: hence, Absolute Convergence of rational series is semi-decidable. A spectral radius-like parameter ρ|r| is introduced, which satisfies the following property: a rational series r is Absolutely convergent iff ρ|r|<1. We show that if r is rational, then ρ|r| can be approximated by convergent upper estimates. Then, it is shown that the sum Σw∈Σ∗|r(w)| can be estimated to any accuracy rate. This result can be extended to any sum of the form Σw∈Σ∗|r(w)|p, for any integer p.

• ##### AbsoluteConvergence of rational series is semi decidable
Language and Automata Theory and Applications, 2009
Co-Authors: Raphael Bailly, Francois Denis

Abstract: