Work

On solving basic equations over the semiring of functional digraphs

Year: 2025

Type: article

Abstract: Endowing the set of functional graphs (FGs) with the sum (disjoint union of graphs) and product (standard direct product on graphs) operations induces on FGs a structure of a commutative semiring R. The operations on R can be naturally extended to the set of univariate polynomials R[X] over R. This paper provides a polynomial time algorithm for deciding if equations of the type AX=B have solutions when A is just a single cycle and B a set of cycles of identical size. We also prove a similar complexity result for some variants of the previous equation. Final version accepted by DMTCS; added a linefeed before 'Clearly' in the before last page, as asked by the editor

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.14590

Authors: Alberto Dennunzio, Enrico Formenti, Luciano Margara, Sara Riva