Using Category Theory to Verify Implementation Against Design in Concurrent Systems

Abstract

The research has shown that process-oriented programming languages provide a suitable means for developing concurrent systems. However, in the development of a concurrent system, there is a challenge to manage consistency between design and implementation. To deal with such a challenge, we propose a new formal verification methodology and illustrate it by a running example. In this methodology, a concurrent system is designed using a process algebra, namely communicating sequential processes, and implemented in a process-oriented programming language, namely Erasmus. The consistency between the design and the implementation of such a concurrent system is verified formally using category theory.

Towards a formal multi-agent organizational modeling framework based on category theory

“…In [19], the authors introduced a MAS categorical generic model, leading to the MAS category. In [20], they introduced a formal verification of a concurrent system based on category theory. In other words, they managed the consistency between design and implementation in the phase of a concurrent system's development.…”

Categorification of the Müller-Wichards System Performance Estimation Model: Model Symmetries, Invariants, and Closed Forms

“…Because of its generality category, theory has found application in recent years in such diverse areas as physics (e.g., [2][3][4][5]), design specification (e.g., [6,7]), data fusion (e.g., [8]), computer science (e.g., [9]), computer security (e.g., [10,11]), systems engineering (e.g., [12]), manufacturing (e.g., [13]), theoretical biology (e.g., [14][15][16]), network theory (e.g., [17]), multi-agent systems models (e.g., [18]), concurrent system design verification (e.g., [19]), emergence (e.g., [20]), and artificial general intelligence (e.g., [21]). Motivated by category theory's mathematical precision and expressive power, this paper introduces a new category theoretic application useful for numerical systems engineering modelling and analysis via a very simple straightforward categorification of MW for the case that the application monoid H is a free monoid generated by a finite set of basis processes, i.e., H is the set of all finite sequences of basis processes, including the empty sequence-where each sequence represents a system and each basis process corresponds to either an arithmetic process, a data movement process, or a delay process-and catenation of systems serves as the associative binary operation.…”

“…A category C is a subcategory of a category D if ( [22], p. 7): every object of C is an object of D; for all objects X, Y of C, Mor C (X, Y) ⊆ Mor D (X, Y); the composition of two morphisms in C is the same as their composition in D; and for all objects X of C, 1 X is the same in D as it is in C. If Obj C is a set, then C is a small category ( [22], p. 6) and if Mor C (X, Y) = ∅ for all X, Y ∈ Obj C , then C is a connected category ( [22], p. 19).…”