Assume-guarantee contract algebras are dp-algebras

Abstract

In [Incer Romeo, I. X., \textit{The Algebra of Contracts}. Ph.D. Thesis, UC Berkeley (2022)] an algebraic perspective on assume-guarantee contracts is proposed. This proposal relies on a construction involving Boolean algebras. However, the structures thus proposed lack a clearly prescribed set of basic operations, necessary if we want to see them as a class of algebras (in the sense of Universal Algebra). In this article, by prescribing a suitable set of basic operations on contracts, we manage to describe these algebras as (a generating set of members of) well-known varieties.

We've changed the category equivalent to AGC to one equivalent to three odd Sugihara monoids. This allows us to provide a direct, less overworked, and self-contained proof of the results from version 1. We've changed the title to fit the new presentation. New citations have been added