The Hadamard product, its residual, and its dual residual in the dioid of counters: algorithms and implementation in C++

TL;DR

This paper introduces algorithms for the Hadamard product and its residuals in the dioid of counters, with implementation in C++ and proofs of correctness, aiding formal power series computations.

Contribution

It presents new algorithms for Hadamard product and residuals in the dioid of counters, along with a C++ implementation and correctness proofs.

Findings

Algorithms are correct and efficient.

C++ implementation is provided in the ETVO toolbox.

The paper includes a user guide for practical use.

Abstract

This report presents the algorithms for computing the Hadamard product, its residual, and its dual residual between formal power series in the dioid of counters. The algorithms have been implemented in the C++ toolbox ETVO ((Event|Time)-Variant Operators). After proving the correctness of the algorithms, we present a user guide for the C++ implementation.