An algebraic approach to weak and delay bismulation in coalgebra

TL;DR

This paper develops an algebraic framework for weak and delay bisimulation in coalgebras, enabling new definitions, properties, and comparisons with existing concepts in coalgebra theory.

Contribution

It introduces an algebraic structure on coalgebras and the final coalgebra, facilitating the formulation and analysis of weak and delay bisimulation concepts.

Findings

Defined algebraic structures for coalgebras and final coalgebra

Characterized a subcoalgebra used in weak coinduction

Compared approximated weak bisimulation with existing notions

Abstract

The aim of this paper is to introduce an algebraic structure on the set of all coalgebras with the same state space over the given type which allows us to present definitions of weak and delay bisimulation for coalgebras. Additionally, we introduce an algebraic structure on the carrier set of the final coalgebra and characterize a special subcoalgebra of the final coalgebra which is used in the formulation of the weak coinduction principle. Finally, the new algebraic setting allows us to present a definition of an approximated weak bisimulation, study its properties and compare it with previously defined weak bisimulation for coalgebras.