A Complete Invariant for Shift Equivalence for Boolean Matrices and Finite Relations

TL;DR

This paper introduces a comprehensive invariant for shift equivalence of Boolean matrices and finite relations, combining period, partial order on recurrent components, and cohomology class, to fully characterize their equivalence.

Contribution

The paper provides a complete invariant for shift equivalence of Boolean matrices and finite relations, advancing the classification theory in this area.

Findings

Complete invariant characterized by period, partial order, and cohomology class.

Invariant fully determines shift equivalence for Boolean matrices.

Framework applicable to finite relations and related structures.

Abstract

We give a complete invariant for shift equivalence for Boolean matrices (equivalently finite relations), in terms of the period, the induced partial order on recurrent components, and the cohomology class of the relation on those components.